Luigi Bianchi

Luigi Bianchi (born January 18, 1856 in Parma , † June 6, 1928 in Pisa ) was an Italian mathematician who mainly dealt with differential geometry .

Life

He studied in Pisa with Enrico Betti and Ulisse Dini together with his friend Gregorio Ricci-Curbastro , who was also to become an important differential geometer and was also a later colleague in Pisa. In 1877 he graduated with honors. After receiving his doctorate, he went to the universities of Munich and to Felix Klein in Göttingen . In 1881 he became a professor at his college in Pisa, the Scuola Normale Superiore , where he received a full professorship in 1890. One of his students was Guido Fubini .

plant

In 1898 he classified the three-dimensional Lie groups of isometries (distance-preserving maps) Riemannian manifolds (and thus the three-dimensional real Lie algebras). These nine groups also later played a role in the symmetry classification of cosmological solutions of general relativity (Bianchi spaces). In 1902 he discovered the Bianchi identities for the Riemann curvature tensor (which Ricci apparently discovered as early as 1880, but which he himself had forgotten), which also play a role in general relativity (they express the conservation of energy). Bianchi also dealt with number theory, where the Bianchi groups are named after him (the analog of the module group above the ring of integers in imaginary quadratic number fields , the projective special linear group ). ${\ displaystyle \ mathbb {Q} ({\ sqrt {-d}})}$ ${\ displaystyle PSL_ {2} (O_ {d})}$

Honors, editorship and memberships

Bianchi had been a corresponding member of the Accademia dei Lincei since 1887 and was elected a full member ( socio nazionale ) in 1893 . For a long time he published the Annali di Matematica . In 1924 he became a senator . He was an honorary member of the London Mathematical Society , since 1920 a corresponding member of the Académie des Sciences and since 1924 of the Göttingen Academy of Sciences . In 1911 he was accepted as a corresponding member of the Russian Academy of Sciences .

Publications (selection)

Lezioni di geometria differenziale , 3 vols., Pisa 1894, 1902, 1909, online , 3rd edition 1922/23
Lectures on differential geometry, Leipzig 1899
Bianchi's lectures on substitution groups, analytical geometry, and function theory in Cornell historical math monographs
Lezioni sulla teoria dei gruppi di sostituzioni e delle equazioni algebriche secondo Galois , Pisa 1900
Lezioni sulla teoria dei gruppi continui finiti di trasformazioni , Pisa 1900
Lezioni sulla teoria dei gruppi di sostituzioni e delle equazioni algebriche secondo Galois , Pisa 1899
Lezioni sulla teoria dei gruppi continui finiti di trasformazioni , Pisa 1918
Lezioni di geometria analitica , Pisa 1915
Lezioni sulla teoria delle funzioni di variabile complessa e delle funzioni ellittiche , Pisa 1916
Lezioni sulla teoria aritmetica delle forme quadratiche binarie e ternarie , Pisa 1912
Lezioni sulla teoria dei numeri algebrici e principii di geometria analitica , Bologna 1923
Geometric representation of the groups of linear substitutions with whole complex coefficients together with application to number theory , Mathematische Annalen, Volume 38, 1891
Sui gruppi di sostituzioni lineari con coefficienti appartenenti a corpi quadratici immaginarî , Mathematische Annalen, Volume 40, 1892, pp. 332–412, SUB Göttingen (Bianchi-Gruppe)
Opere , Edizioni Cremonese, Rome, 11 volumes, 1952 to 1959 (with bibliography and analysis of his scientific work in volume 1 by G. Scorza, Guido Fubini, AM Bedarida and G. Ricci)

literature

Enzo Pozzato: Bianchi, Luigi. In: Alberto M. Ghisalberti (Ed.): Dizionario Biografico degli Italiani (DBI). Volume 10: Biagio-Boccaccio. Istituto della Enciclopedia Italiana, Rome 1968.
Wilhelm Blaschke : Luigi Bianchi e la geometria differenziale . In: Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Ser. 3, 8 no. 1-2 (1954), pp. 43–52 ( online at NUMDAM, PDF)
Ettore Carruccio: Article Luigi Bianchi in Dictionary of Scientific Biography
Guido Fubini : Luigi Bianchi e la sua opera scientifica , Annali di matematica, Volume 6, 1928/29, pp. 45-83
Guido Fubini: Commemorazione di Luigi Bianchi , Rendiconti della Accademia nazionale dei Lincei, Classe di scienze fisiche matematiche e naturali, Series 6a, Volume 10, 1929, pp. Xxxiv-xliv
H. Hilton Luigi Bianchi , Journal of the London Mathematical Society, Volume 4, 1929, pp. 79-80

Web links

Entry in the Archivio Storico of the Italian Senate: Senatori d'Italia. III. Senatori dell'Italia Fascista
John J. O'Connor, Edmund F. Robertson : Luigi Bianchi. In: MacTutor History of Mathematics archive .
On Bianchi's work in the context of general relativity

Individual evidence

^ B. Fine, Bianchi group , Encyclopedia of Mathematics, Springer
↑ Holger Krahnke: The members of the Academy of Sciences in Göttingen 1751-2001 (= Treatises of the Academy of Sciences in Göttingen, Philological-Historical Class. Volume 3, Vol. 246 = Treatises of the Academy of Sciences in Göttingen, Mathematical-Physical Class. Episode 3, vol. 50). Vandenhoeck & Ruprecht, Göttingen 2001, ISBN 3-525-82516-1 , p. 40.
^ Foreign members of the Russian Academy of Sciences since 1724: Bianchi, Luigi. Russian Academy of Sciences, accessed September 19, 2019 (in Russian).

personal data
SURNAME	Bianchi, Luigi
BRIEF DESCRIPTION	Italian mathematician
DATE OF BIRTH	January 18, 1856
PLACE OF BIRTH	Parma
DATE OF DEATH	June 6, 1928
Place of death	Pisa

[1] B. Fine, Bianchi group , Encyclopedia of Mathematics, Springer

[2] Holger Krahnke: The members of the Academy of Sciences in Göttingen 1751-2001 (= Treatises of the Academy of Sciences in Göttingen, Philological-Historical Class. Volume 3, Vol. 246 = Treatises of the Academy of Sciences in Göttingen, Mathematical-Physical Class. Episode 3, vol. 50). Vandenhoeck & Ruprecht, Göttingen 2001, ISBN 3-525-82516-1 , p. 40.

[3] Foreign members of the Russian Academy of Sciences since 1724: Bianchi, Luigi. Russian Academy of Sciences, accessed September 19, 2019 (in Russian).