Luigi Bianchi (January 18 1856 - June 6 1928) was an Italian mathematician. He was born in Parma, Emilia-Romagna, and died in Pisa. He was a leading member of the vigorous geometric school which flourished in Italy during the later years of the 19th century and the early years of the twentieth century. Like his friend and colleague Gregorio Ricci-Curbastro, Bianchi studied at the Scuola Normale Superiore in Pisa under Enrico Betti, a leading differential geometer who is today best remembered for his seminal contributions to topology, and Ulisse Dini, a leading expert on function theory. Bianchi was also greatly influenced by the geometrical ideas of Bernhard Riemann and by the work on transformation groups of Sophus Lie and Felix Klein. Bianchi became a professor at the Scuola Normale Superiore in Pisa in 1896, where he spent the remainder of his career. At Pisa, his colleagues included the talented Ricci. In 1890, Bianchi and Dini supervised the dissertation of the noted analyst and geometer Guido Fubini.

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  • Luigi Bianchi (January 18 1856 - June 6 1928) was an Italian mathematician. He was born in Parma, Emilia-Romagna, and died in Pisa. He was a leading member of the vigorous geometric school which flourished in Italy during the later years of the 19th century and the early years of the twentieth century. Like his friend and colleague Gregorio Ricci-Curbastro, Bianchi studied at the Scuola Normale Superiore in Pisa under Enrico Betti, a leading differential geometer who is today best remembered for his seminal contributions to topology, and Ulisse Dini, a leading expert on function theory. Bianchi was also greatly influenced by the geometrical ideas of Bernhard Riemann and by the work on transformation groups of Sophus Lie and Felix Klein. Bianchi became a professor at the Scuola Normale Superiore in Pisa in 1896, where he spent the remainder of his career. At Pisa, his colleagues included the talented Ricci. In 1890, Bianchi and Dini supervised the dissertation of the noted analyst and geometer Guido Fubini. In 1898, Bianchi worked out the Bianchi classification of nine possible isometry classes of three-dimensional Lie groups of isometries of a Riemannian manifold. As Bianchi knew, this is essentially the same thing as classifying, up to isomorphism, the three-dimensional real Lie algebras. This complements the earlier work of Lie himself, who had earlier classified the complex Lie algebras. Through the influence of Luther P. Eisenhart and Abraham Haskel Taub, Bianchi's classification later came to play an important role in the development of the theory of general relativity. Bianchi's list of nine isometry classes, which can be regarded as Lie algebras, Lie groups, or as three dimensional homogeneous Riemannian manifolds, are now often called collectively the Bianchi groups. In 1902, Bianchi rediscovered what are now called the Bianchi identities for the Riemann tensor, which play an even more important role in general relativity. According to Tullio Levi-Civita, these identities had first been discovered by Ricci in about 1880, but Ricci apparently forgot all about the matter, which led to Bianchi's rediscovery! (en)
  • Come il suo amico e collega Gregorio Ricci-Curbastro, Bianchi studiò alla Scuola Normale Superiore di Pisa con Enrico Betti, un eminente studioso di geometria e algebra, che oggi è ricordato per i suoi contributi fondanti alla topologia e con Ulisse Dini, altra figura di spicco esperto di teoria delle funzioni. Bianchi fu fortemente influenzato anche dalle idee sulla geometria di Bernhard Riemann e dal lavoro sui gruppi di Lie di Sophus Lie e Felix Klein. Bianchi divenne docente alla Normale di Pisa nel 1896, dove trascorse il resto della sua carriera. A Pisa, tra i suoi colleghi c'era anche il talentuoso Ricci. Nel 1890 Bianchi e Dini supervisionarono la dissertazione del noto esperto di analisi e geometria Guido Fubini. Nel 1898, Bianchi elaborò la famosa classificazione di Bianchi delle nove possibili classi di isometrie delle varietà riemanniane di tre dimensioni, che equivale a classificare gli isomorfismi di un'algebra di Lie tridimensionale e reale, completando così il lavoro di Lie stesso, che aveva classificato le algebre complesse. Grazie al lavoro di Luther P. Eisenhart e Abraham Haskel Taub, la classificazione giocò un ruolo importante nello sviluppo della teoria della relatività generale. Le nove classi di isometrie, che possono riguardare l'algebra di Lie, i gruppi di Lie o le varietà riemanniane a tre parametri, sono spesso chiamate collettivamente gruppo di Bianchi. Nel 1902, Bianchi riscoprì quelle che oggi si chiamano identità di Bianchi per il tensore di Riemann, che hanno un ruolo molto importante nella relatività generale (sono essenziali per capire le equazioni di campo di Einstein); queste identità erano state trovate da Ricci per primo attorno al 1880, ma accantonate da lui stesso. (it)
  • Luigi Bianchi (* 18. Januar 1856 in Parma; † 6. Juni 1928 in Pisa) war ein italienischer Mathematiker, der sich vor allem mit Differentialgeometrie beschäftigte. Er studierte in Pisa bei Enrico Betti und Ulisse Dini zusammen mit seinem Freund Gregorio Ricci-Curbastro, der ebenfalls ein bedeutender Differentialgeometer werden sollte und auch ein späterer Kollege in Pisa war. 1877 schloss er sein Studium mit Auszeichnung ab. Nach seiner Promotion ging er an die Universitäten von Monaco und zu Felix Klein nach Göttingen. 1881 wurde er Professor an seiner Universität in Pisa, der Scuola Normale Superiore, wo er 1890 eine volle Professur erhielt. Einer seiner Schüler war Guido Fubini. 1898 klassifizierte er die dreidimensionalen Liegruppen von Isometrien Riemannscher Mannigfaltigkeiten . Diese neun Bianchi Gruppen spielten auch später eine Rolle in der Symmetrie-Klassifikation von kosmologischen Lösungen der Allgemeinen Relativitätstheorie. 1902 entdeckte er die Bianchi-Identitäten für den Riemannschen Krümmungstensor, die ebenfalls eine Rolle in der Allgemeinen Relativitätstheorie spielen (sie drücken die Energieerhaltung aus). Bianchi beschäftigte sich auch mit Zahlentheorie. Bianchi war ab 1893 Mitglied der Accademia dei Lincei und gab lange Zeit die Annali di Matematica heraus. (de)
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  • Ettore (en)
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  • Carruccio (en)
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  • Bianchi, Luigi (en)
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  • Luigi Bianchi (January 18 1856 - June 6 1928) was an Italian mathematician. He was born in Parma, Emilia-Romagna, and died in Pisa. He was a leading member of the vigorous geometric school which flourished in Italy during the later years of the 19th century and the early years of the twentieth century. Like his friend and colleague Gregorio Ricci-Curbastro, Bianchi studied at the Scuola Normale Superiore in Pisa under Enrico Betti, a leading differential geometer who is today best remembered for his seminal contributions to topology, and Ulisse Dini, a leading expert on function theory. Bianchi was also greatly influenced by the geometrical ideas of Bernhard Riemann and by the work on transformation groups of Sophus Lie and Felix Klein. Bianchi became a professor at the Scuola Normale Superiore in Pisa in 1896, where he spent the remainder of his career. At Pisa, his colleagues included the talented Ricci. In 1890, Bianchi and Dini supervised the dissertation of the noted analyst and geometer Guido Fubini. (en)
  • Come il suo amico e collega Gregorio Ricci-Curbastro, Bianchi studiò alla Scuola Normale Superiore di Pisa con Enrico Betti, un eminente studioso di geometria e algebra, che oggi è ricordato per i suoi contributi fondanti alla topologia e con Ulisse Dini, altra figura di spicco esperto di teoria delle funzioni. (it)
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  • Luigi Bianchi (en)
  • Luigi Bianchi (fr)
  • Luigi Bianchi (it)
  • Luigi Bianchi (de)
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