Italian mathematician

Giovanni Battista Rizza (born 7 February 1924) (at the registry office Giambattista Rizza) is an Italian mathematician, working in the fields of complex *ysis of several variables and in differential geometry: he is known for his contribution to hypercomplex *ysis, notably for extending Cauchy's integral theorem and Cauchy's integral formula to complex functions of a hypercomplex variable, the theory of pluriharmonic functions and for the introduction of the now called Rizza manifolds.

Contents

• 1 Biography
  • 1.1 Life and academic career
  • 1.2 Honors
  • 1.3 Personality traits
• 2 Work
  • 2.1 Research activity
    • 2.1.1 Theory of functions on algebras
    • 2.1.2 Theory of *ytic functions of several complex variables
• 3 Selected publications
  • 3.1 Research works
  • 3.2 Historical, commemorative and survey papers
• 4 See also
• 5 Notes
• 6 References
  • 6.1 Biographical sources
  • 6.2 Scientific references

Biography

The International Symposium on Algebraic Geometry held in Rome in 1965. Enrico Bompiani talking to Giovanni Battista Rizza and Vittorio Dalla Volta.

Life and academic career

Born in Piazza Armerina, the son of Giovanni and Angioletta Bocciarelli, he graduated from the Università degli Studi di Genova, earning his laurea degree in 1949 under the direction of Enzo Martinelli. In 1956 he was in Rome at the INdAM, having been awarded a scholarship for his early research activities. A year later, in 1957, he was elected "discepolo ricercatore" in the same ins*ute. During the same year, he gave some lectures on topics belonging to the field of several complex variables, later included in the lecture notes (Severi 1958). In Rome he also met Lucilla B*otti, who eventually become his wife. In 1961, he won the compe*ive examination for the chair of "Geometria *itica con elementi di Geometria Proiettiva e Geometria Descrittiva con Disegno" of the University of Parma, scoring first out of the three finalists: a year later, in 1962, he became extraordinary professor, and then, in 1965, ordinary professor to the same chair. In 1979 he became ordinary professor of "Geometria superiore", holding that chair uninterruptedly until 1994: from 1994 up to his retirement in 1997, he was "professore fuori ruolo" in the same department of mathematics where he worked for more than 35 years.

Apart from his research and teaching work, he was actively involved as a member of the editorial board of the "Rivista di Matematica della Università di Parma", and served also as the journal director from 1992 to 1997.

Honors

In 1954 he was awarded the Ottorino Pomini prize by the Unione Matematica Italiana, jointly with Gabriele Darbo: the judging commission was composed by Giovanni Sansone (as the president), Alessandro Terracini, Beniamino Segre, Giuseppe Scorza-Dragoni, Carlo Miranda, Mario Villa and Enzo Martinelli (as the secretary).

In 1973 he was awarded the golden medal "Benemeriti della Scuola, della Cultura, dell'Arte" by the President of the Italian Republic, as an acknowledgement his research and teaching and achievements as civil servant at the University of Parma.

In 1995, to celebrate his 70th birthday, an international conference on differential geometry was organized in Parma: the proceedings were later published as a special issue of the "Rivista di Matematica della Università di Parma".In 1999 the University of Parma, where he worked for more than 35 years, awarded him the *le of professor emeritus.

He is currently an honorary member of the Balkan Society of Geometers and life member of the Tensor Society.

Personality traits

Enzo Martinelli describes Giovanni Battista Rizza as a p*ionate researcher with a "strong intellectual force", and his scientific work as rich of geometrical ideas, denoting his strong algorithmic ability. According to Martinelli, Rizza is also a skilled organizer: his ability in organizational tasks is also acknowledged and praised by Schreiber (1973, p.:1), who also alludes the positive opinions of colleagues and students alike about his involvement in research, teaching and administrative duties at the mathematics department of the University of Parma.

Work

Research activity

Giovanni Battista Rizza has aut*d 53 research papers and 30 other scientific works, including research announcements, short notes, surveys and reports: he also wrote didactic notes and papers on historical topics, including commemorations of other scientists. His main fields of research are the theory of functions on algebras, the theory of functions of several complex variables, and differential geometry.

Theory of functions on algebras

The theory of functions on algebras, also referred to as hypercomplex *ysis, is the study of functions whose domain is a subset of an algebra. The first works of Giovanni Battista Rizza belong to this field of research, and he was awarded the Premio Ottorino Pomini for his contributions.

His first main result is the extension of Cauchy's integral theorem to every monogenic function F on a general complex algebra A,

∫ Γ 1 F ( X ) d X = 0 {displaystyle int _{Gamma _{1}}mathrm {F} (mathrm {X} )mathrm {d} mathrm {X} =0}

where Γ1 is a 1-dimensional cycle *logous to zero, and also satisfying other technical conditions.

Few years later, he extended Cauchy's integral formula to every monogenic function F on a commutative normed real algebra A*, isomorphic to a given complex algebra A: precisely, he proves the formula

∫ Γ 1 F ( X ) X − Ξ d X = 2 π i ∑ s = 1 k N ( s ) u ( s ) F ( Ξ ) {displaystyle int _{Gamma _{1}}{frac {mathrm {F} (mathrm {X} )}{mathrm {X} -Xi }}mathrm {d} mathrm {X} =2pi isum _{s=1}^{k}mathrm {N} ^{(s)}u^{(s)}mathrm {F} (Xi )}

where

• X:≡:x*:≡:x identifies indifferently a point in the complex algebra A or in its isomorphic real algebra A*,
• Γ1 is again a 1-dimensional cycle *logous to zero, and satisfying other technical conditions,
• N(s) is the winding number of the cycle Γ1 respect to the zero divisor locus for the considered algebra.

Theory of *ytic functions of several complex variables

All'estensione, tutt'altro che b*e, allo spazio R2n dei metodi di Martinelli per dimostrare la (3), è dedicata una Memoria di Giovanni Battista Rizza, il quale, sempre nell'ipotesi ρ(x1,:y1,...,:xn,:yn):∈:Cω, perviene a stabilire la (3) per n qualsiasi. Anche questo lavoro, per quanto redatto in lingua inglese e pubblicato su una delle principali riviste matematiche, non ha nella letteratura attuale, la notorietà che meriterebbe.

— Gaetano Fichera, (Fichera 1982a, p.:135).

Rizza published only three work in this field: in the first one, the highly remarkable memoir (Rizza 1955), he extends to pluriharmonic functions of 2n real variables, n:>:2, the methods introduced by Enzo Martinelli in order to give new proof of a result of Luigi Amoroso for pluriharmonic functions of four real variables. Precisely, he proves the following formula

(1)

where

• u is a polyharmonic function defined on a bounded domain Ω,
• ρ is a real *ytic function defining the boundary of Ω by the equation

∂ Ω = { x ∈ R 2 n | ρ ( x ) = 0 } , {displaystyle partial Omega ={xin mathbb {R} ^{2n}|rho (x)=0},}

• Q(ρ) is a linear combination of the Levi forms of ρ relative to couples of complex variables,
• E is a linear tangential operator defined on ∂Ω.

Formula (1) express a condition the normal derivative of the boundary value of a pluriharmonic function on domain with real *ytic boundary must satisfy. It can be used to construct an integral representation for pluriharmonic functions on such kind of domains, by using the Green's formula for the Laplacian, and also to establish an integro-differential equation boundary values of pluriharmonic functions must satisfy. Rizza's result motivated other works on the same topic by Gaetano Fichera, Paolo de Bartolomeis and Giuseppe Tom*ini.

Selected publications

Research works

• Rizza, Giovanni Battista (1950), "Sulle funzioni *itiche nelle algebre ipercomplesse", Pontificia Academia Scientiarum. Commentationes (in Italian), 14: 169–194, MR:0057350. In "On *ytic functions on hypercomplex algebras" (English translation of the *le), Rizza extends the cl*ical Cauchy's integral theorem to monogenic functions on a general complex algebra.
• Rizza, Giovanni Battista (1952), "Contributi al problema della determiNational Socialist German Workers' Partyone di una formula integrale per le funzioni monogene nelle algebre complesse dotate di modulo e commutative", Rendiconti di Matematica, V Serie (in Italian), 23 (1–2): 134–155, MR:0211370, Zbl:0047.32204. "Contributions to the problem of determining an integral formula for monogenic functions on complex commutative algebras with modulus" (English translation of the *le).
• Rizza, Giovanni Battista (1952a), "Estensione della formula integrale di Cauchy alle algebre complesse dotate di modulo e commutative", Rendiconti della Accademia National Socialist German Workers' Partyonale dei Lincei, Cl*e di Scienze Fisiche, Matematiche e Naturali, Serie VIII (in Italian), XII (6): 667–669, MR:0062240, Zbl:0048.06101. "Extension of Cauchy's integral formula to commutative complex algebras with modulus" (English translation of the *le).
• Rizza, Giovanni Battista (1953), "Teoria delle funzioni nelle algebre complesse dotate di modulo e commutative", Rendiconti di Matematica, V Serie (in Italian), 23 (1–2): 221–249, MR:0211370, Zbl:0123.15203. "Function theory on commutative complex algebras with modulus" (English translation of the *le).
• Rizza, Giovanni Battista (1954), "On Dirichlet's problem for components of *ytic functions of several complex variables" (PDF), Proceedings of the International Congress of Mathematicians, 1954. Volume II, ICM Proceedings, Amsterdam–Groningen: Erven P. Noordhoff N.V. / North-Holland Publishing Company, pp.:161–162. A short research announcement describing briefly the results proved in (Rizza 1955).
• Rizza, G. B. (1955), "Dirichlet problem for n-harmonic functions and related geometrical problems", Mathematische Annalen, 130 (3): 202–218, doi:10.1007/BF01343349, MR:0074881, S2CID:121147845, Zbl:0067.33004, available at DigiZeitschirften.
• Rizza, G. B. (1957), "Su diverse estensioni dell'invariante di E. E. Levi nella teoria delle funzioni di più variabili complesse", Annali di Matematica Pura ed Applicata (in Italian), 44 (1): 73–89, doi:10.1007/BF02415191, MR:0095965, S2CID:120897623, Zbl:0091.25903. In the work "On different extensions of E. E. Levi invariant in the theory of functions of several complex variables" (English translation of the *le), Rizza epitomizes all known extensions of the Levi invariant to hypersurfaces in ℂn for n:>:2 in a single tensor of hybrid type. This paper is also interesting since it traces the story of such extensions back to the pioneering work of Eugenio Elia Levi.
• Rizza, G. B. (1958), "Appendice I. Rappresentazione esplicita di tipo integrale per le funzioni r–armoniche. Estensione al caso di r variabili complesse dell'invariante di E. E. Levi", in Severi, Francesco (ed.), Lezioni sulle funzioni *itiche di più variabili complesse – Tenute nel 1956–57 all'Is*uto National Socialist German Workers' Partyonale di Alta Matematica in Roma (in Italian), Padova: CEDAM – Casa Editrice Dott. Antonio Milani, pp.:219–231, Zbl:0094.28002. The notes from the lectures given by Giovanni Battista Rizza for the course "Lectures on *ytic functions of several complex variables", held by Francesco Severi at the Is*uto National Socialist German Workers' Partyonale di Alta Matematica: the full course notes, published as a monograph, include also a chapter by Enzo Martinelli and an appendix by Mario Benedicty). The topics he exposes are summarized by the two parts of the *le, whose English translations are "Explicit integral representation for r {displaystyle r} –harmonic functions" and "Extension of the E. E. Levi invariant to the case of r {displaystyle r} complex variables".
• Rizza, Giovanni Battista (1962a), "Finsler structures on almost complex manifolds", Proceedings of the International Congress of Mathematicians, Stockholm., ICM Proceedings, Stockholm. A short research announcement describing briefly the results proved in (Rizza 1963).
• Rizza, Giovanni Battista (1962b), "Strutture di Finsler sulle varietà quasi complesse", Rendiconti della Accademia National Socialist German Workers' Partyonale dei Lincei, Cl*e di Scienze Fisiche, Matematiche e Naturali, Serie VIII (in Italian), 33 (5): 271–275. "Finsler structures on almost complex manifolds" (English translation of the *le) is another short presentation of the results proved in (Rizza 1963).
• Rizza, Giovanni Battista (1963), "Strutture di Finsler di tipo quasi Hermitiano", Rivista di Matematica della Università di Parma, (2) (in Italian), 4: 83–106, MR:0166742, Zbl:0129.14101, archived from the original on March 16, 2012. The article giving the proofs of the results previously announced in references (Rizza 1962a) and Rizza (1962b): the English translation of the *le reads as: "Finsler structures of almost Hermitian type".
• Rizza, Giovanni Battista (1964), "F-forme quadratiche ed hermitiane", Rendiconti di Matematica, V Serie (in Italian), 23 (1–2): 221–249, MR:0211370, Zbl:0123.15203. This article is the one Shoshichi Kobayashi cites as the first one in the theory of Rizza manifolds: an English translation of the *le reads as: "Hermitian and quadratic F-forms".
• Rizza, Giovanni Battista (1969), "Teoremi di rappresentazione per alcune cl*i di connessioni su di una varietà quasi complessa" (PDF), Rendiconti dell'Is*uto di Matematica dell'Università di Trieste (in Italian), 1: 9–25, MR:0257917, Zbl:0183.50701.
• Rizza, Giovanni Battista (1969), "Connessioni metriche sulle varietà quasi hermitiane" (PDF), Rendiconti dell'Is*uto di Matematica dell'Università di Trieste (in Italian), 1: 9–25, MR:0262995, Zbl:0192.58903.
• Dentoni, Paolo; Rizza, Giovanni Battista (1972), "Una nuova cl*e di funzioni in un'algebra reale" (PDF), Rendiconti dell'Is*uto di Matematica dell'Università di Trieste (in Italian), 4: 171–181, MR:0492318, Zbl:0251.30050. "A new cl* of functions on a real algebra" (English translation of the *le) the authors introduce a new cl* of functions on a real algebra in the attempt of unifying the research trends on functions on real algebras in the seventies.

Historical, commemorative and survey papers

• Rizza, Giovanni Battista (December 12, 1973), "Contributi recenti alla teoria delle funzioni nelle algebre", Rendiconti del Seminario Matematico e Fisico di Milano (in Italian), 43 (1): 45–54, doi:10.1007/BF02924838, MR:0350025, S2CID:123219540, Zbl:0325.30040. "Recent contributions to the theory of functions on algebras" (English translation of the *le) is a short but comprehensive survey paper detailing the works on the field done by Italian mathematicians during the years from 1961 to 1973: however, it also includes several biographical references to other earlier works by non Italian mathematicians and to historical bibliographies on hypercomplex *ysis.
• Rizza, Giovanni Battista (1986), "Indirizzo di adesione", in Montalenti, G.; Amerio, L.; Acquaro, G.; Baiada, E.; Cesari, L.; Ciliberto, C.; Cimmino, G.; Cinquini, S.; De Giorgi, E.; Faedo, S.; Fichera, G.; Galligani, I.; Ghizzetti, A.; Graffi, D.; Greco, D.; Grioli, G.; Magenes, E.; Martinelli, E.; Pettineo, B.; Scorza, G.; Vesentini, E. (eds.), Convegno celebrativo del centenario della nascita di Mauro Picone e Leonida Tonelli (6–9 maggio 1985), Atti dei Convegni Lincei, vol.:77, Roma: Accademia National Socialist German Workers' Partyonale dei Lincei, pp.:29–30, archived from the original on February 23, 2011, retrieved February 16, 2014. The brief "participating address" presented to the International congress on the occasion of the celebration of the centenary of birth of Mauro Picone and Leonida Tonelli (held in Rome on May 6–9, 1985), by Giovanni Battista Rizza on behalf of the University of Parma: the scientific relations between Leonida Tonelli and the Department of Mathematics in Parma are described.
• Rizza, Giovanni Battista (1984), "Enzo Martinelli: Scienziato e Maestro" (PDF), Rivista di Matematica della Università di Parma, (4) (in Italian), 10*: 1–10, MR:0777308, Zbl:0557.01011. "Enzo Martinelli: Scientist and Master" (English translation of the *le) is a celebrative paper written by Giovanni Battista Rizza to honor his former master.
• Rizza, Giovanni Battista (1998), "Commemorazione del Prof. Francesco Speranza" (PDF), Rivista di Matematica della Università di Parma, (6) (in Italian), 1: 225–230, MR:1680985.
• Rizza, Giovanni Battista (1999), "Commemorazione della professoressa Bianca Manfredi" (PDF), Rivista di Matematica della Università di Parma, (6) (in Italian), 2: 213–215, MR:1753340, Zbl:1073.01521.
• Rizza, Giovanni Battista (April 2002), "Commemorazione di Enzo Martinelli" , Bollettino dell'Unione Matematica Italiana. Sezione A. La Matematica nella Società e nella Cultura, Serie VIII (in Italian), 5-A: 163–176, MR:1924344, Zbl:1194.01133.

See also

• Almost complex manifold
• Complex manifold
• Kähler manifold
• Pluriharmonic function
• Pseudoconvexity
• Rizza manifold
• Several complex variables

Notes

References

Biographical sources

• Balkan Society of Geometers (July 24, 2011), The list of members of the Balkan Society of Geometers (PDF), retrieved April 19, 2011.
• Bollettino UMI (1954), "Notizie (Notices)", Bollettino dell'Unione Matematica Italiana, Serie III (in Italian), 9 (4): 467–490. The official relation of the judging commission for the awarding of the Ottorino Pomini Prize in 1954, jointly won by Gabriele Darbo and Giovanni Battista Rizza.
• Bollettino UMI (1962), "Notizie (Notices)", Bollettino dell'Unione Matematica Italiana, Serie III (in Italian), 17 (1): 120–157. The official announcement of the winning by Giovanni Battista Rizza of the chair of "Geometria *itica con elementi di Geometria Proiettiva e Geometria Descrittiva con Disegno" awarded by the University of Parma.
• The Editorial Board, ed. (1965), "Professori ordinari", Annuario dell'Università di Parma, vol.:A.A. 1964/1965, Parma: Università degli Studi di Parma.
• The Editorial Board, ed. (1980), "Professori ordinari", Annuario dell'Università di Parma, vol.:A.A. 1979/80, Parma: Università degli Studi di Parma.
• The Editorial Board, ed. (1995), "Professori ordinari", Annuario dell'Università di Parma, vol.:A.A. 1994/95, Parma: Università degli Studi di Parma.
• Martinelli, E. (1994), "Omaggio a Giovanni Battista Rizza in occasione del suo 70° compleanno" (PDF), in Donnini, S.; Gigante, G.; Mangione, V. (eds.), Geometria differenziale – *isi complessa. Convegno interNational Socialist German Workers' Partyonale – Parma, 19–20 maggio 1994 in occasione del 70° compleanno di G. B. Rizza, 5a Serie (in Italian), vol.:3, Rivista di Matematica della Università di Parma, pp.:1–2. "Homage to Giovanni Battista Rizza on his 70th birthday" (English translation of the *le) a tribute to Giovanni Battista Rizza by his former master Enzo Martinelli.
• Il Ministro dell'Università e della Ricerca Scientifica e Tecnologica (February 19, 1999), Decreto Ministeriale 17 Febbraio 1999 (in Italian). The "Ministerial Decree" awarding the *le of "Professor Emeritus" to Giovanni Battista Rizza.
• Presidenza della Repubblica Italiana (July 31, 1973), Medaglia d'oro ai benemeriti della scuola della cultura e dell'arte: Giovanni Battista Rizza, retrieved May 31, 2011.
• Rivista di Matematica della Università di Parma, (the Editorial Board of) (December 12, 2013), History, retrieved January 12, 2013.
• Roghi, G. (December 2005), "Materiale per una storia dell'Is*uto National Socialist German Workers' Partyonale di Alta Matematica dal 1939 to 2003.", Bollettino della Unione Matematica Italiana, Sezione A, La Matematica nella Società e nella Cultura, Serie VIII (in Italian), 8-A (3, parte 2): x+301, MR:2225078, Zbl:1089.01500. "Materials toward a history of the Is*uto National Socialist German Workers' Partyonale di Alta Matematica from 1939 to 2003" (English translation of *le) is a monographic fascicle published on the "Bollettino della Unione Matematica Italiana", describing the history of the Is*uto National Socialist German Workers' Partyonale di Alta Matematica Francesco Severi from its foundation in 1939 to 2003. It was written by Gino Roghi and includes a presentation by Salvatore Coen and a preface by Corrado De Concini. It is almost exclusively based on sources from the ins*ute archives: the wealth and variety of materials included, jointly with its appendices and indexes, make this monograph a useful reference not only for the history of the ins*ute itself, but also for the history of many mathematicians who taught, followed the ins*ute courses or simply worked there.
• Schreiber, Bruno (1973), Curriculum Vitæ di Giambattista Rizza (in Italian), Is*uto di Matematica dell'Università di Parma, p.:4. The official 1973 CV of Giovanni Battista Rizza, available from the Ins*ute of Mathematics of the University of Parma.
• Tensor Society (2010), List of life members of the Tensor Society (PDF), retrieved July 14, 2013.
• Venturini, Giancarlo (1963), "Prolusione all'apertura dell'A.A. 1962/63", Annuario dell'Università di Parma, vol.:A.A. 1962/63, Parma: Università degli Studi di Parma. The opening address on the occasion of the beginning of the academic year 1962/63, given by the Magnifico Rettore prof. G. Venturini.

Scientific references

• Aikou, Tadashi (2004), "Finsler Geometry on Complex Vector Bundles" (PDF), in Bao, David; Bryant, Robert L.; Chern, Shiing-Shen; Shen, Zhongmin (eds.), A Sampler of Riemann–Finsler Geometry, Mathematical Sciences Research Ins*ute Publications, vol.:50, Cambridge: Cambridge University Press, pp.:83–105, Bibcode:2004srfg.book.....B, ISBN:978-0-521-83181-9, MR:2132658, Zbl:1073.53093.
• de Bartolomeis, Paolo; Tom*ini, Giuseppe (1981), "Traces of pluriharmonic functions", Compositio Mathematica, 44 (1–3): 29–39, MR:0662454, Zbl:0484.32007.
• Donnini, S.; Gigante, G.; Mangione, V., eds. (1994), "Geometria differenziale – *isi complessa. Convegno interNational Socialist German Workers' Partyonale – Parma, 19–20 maggio 1994 in occasione del 70° compleanno di G. B. Rizza", Rivista di Matematica della Università di Parma, Serie 5, 3 (Parte I). The proceedings of the international meeting "Differential Geometry – Complex *ysis" held in Parma on May 19–20, 1994 to celebrate Giovanni Battista Rizza's 70th birthday, published by the Rivista di Matematica della Università di Parma. The first speaker was his former master Enzo Martinelli.
• Fichera, Gaetano (1982a), "Problemi al contorno per le funzioni pluriarmoniche", Atti del Convegno celebrativo dell'80° anniversario della nascita di Renato Calapso, Messina–Taormina, 1–4 aprile 1981 (in Italian), Roma: Libreria Eredi Virgilio Veschi, pp.:127–152, MR:0698973, Zbl:0958.32504. "Boundary value problems for pluriharmonic functions" (English translation of the *le) deals with boundary value problems for pluriharmonic functions: Fichera gives a trace condition for the solvability of the problem and extensively reviews its history, starting from its beginning in the work of Henri Poincare and *yzing several earlier results of Enzo Martinelli, Giovanni Battista Rizza and Francesco Severi, as well as works of Aldo Andreotti among the others.
• Fichera, Gaetano (1982b), "Valori al contorno delle funzioni pluriarmoniche: estensione allo spazio R2n di un teorema di L. Amoroso", Rendiconti del Seminario Matematico e Fisico di Milano (in Italian), 52 (1): 23–34, doi:10.1007/BF02924996, MR:0802991, S2CID:122147246, Zbl:0569.31006. In the work "Boundary values of pluriharmonic functions: extension to the space R2n of a theorem of L. Amoroso" (English translation of the *le), Gaetano Fichera proves anothera trace condition for pluriharmonic functions and surveys other recent works in the fields, notably the one of de Bartolomeis & Tom*ini (1981).
• *, B. A. (1963), Introduction to the Theory of *ytic Functions of Several Complex Variables, Translations of Mathematical Monographs, vol.:8, Providence, RI: American Mathematical Society, pp.:vi+374, ISBN:9780821886441, MR:0168793, Zbl:0138.30902.
• Ichijyō, Yoshihiro (1988), "Finsler metrics on almost complex manifolds", Rivista di Matematica della Università di Parma, (IV), 14*: 1–28, MR:1045035, Zbl:0885.53031, archived from the original on March 16, 2012.
• Kobayashi, Shoshichi (1975), "Negative vector bundles and complex Finsler structures", Nagoya Mathematical Journal, 57: 153–166, doi:10.1017/S0027763000016615, MR:0377126, Zbl:0326.32016. In this paper, Shoshichi Kobayashi acknowledges Giovanni Battista Rizza as the first one to study complex manifolds with Finsler structure, now called Rizza manifolds.
• Martinelli, Enzo (1941), "Studio di alcune questioni della teoria delle funzioni biarmoniche e delle funzioni *itiche di due variabili complesse coll'ausilio del calcolo differenziale *oluto", Atti della Reale Accademia d'Italia. Memorie della Cl*e di Scienze Fisiche, Matematiche e Naturali (in Italian), 12 (4): 143–167, JFM:67.0299.01, MR:0017810, Zbl:0025.40503. In "Study of some questions of the theory of biharmonic functions and of *ytic functions of two complex variables by using the absolute differential calculus" (English translation of *le) Martinelli proves an earlier result of Luigi Amoroso on the boundary values of pluriharmonic function by using tensor calculus.
• Scharnhorst, K. (2001), "Angles in Complex Vector Spaces", Acta Applicandae Mathematicae, 69 (1): 95–103, arXiv:math/9904077, doi:10.1023/A:1012692601098, MR:1868915, S2CID:17284421, Zbl:0993.51010.
• Severi, Francesco (1958), Lezioni sulle funzioni *itiche di più variabili complesse – Tenute nel 1956–57 all'Is*uto National Socialist German Workers' Partyonale di Alta Matematica in Roma (in Italian), Padova: CEDAM – Casa Editrice Dott. Antonio Milani, pp.:XIV+255, Zbl:0094.28002. The "Lectures on *ytic functions of several complex variables – Lectured in 1956–57 at the Is*uto National Socialist German Workers' Partyonale di Alta Matematica in Rome" (English translation of the *le) is a set of lecture notes from a course held by Francesco Severi at the Is*uto National Socialist German Workers' Partyonale di Alta Matematica, including appendices of Enzo Martinelli, Giovanni Battista Rizza and Mario Benedicty.