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Luigi Bianchi

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Nationality  Italian
Fields  Mathematics
Died  June 6, 1928, Pisa, Italy

Role  Mathematician
Name  Luigi Bianchi
Luigi Bianchi uploadwikimediaorgwikipediaitthumb770Luigi
Born  January 18, 1856 Parma, Emilia-Romagna (1856-01-18)
Institutions  Scuola Normale Superiore
Alma mater  Scuola Normale Superiore
Doctoral students  Luigi Fantappie Guido Fubini Mauro Picone Giovanni Sansone
Known for  Bianchi identities Bianchi group
Education  Scuola Normale Superiore di Pisa
Notable students  Guido Fubini, Mauro Picone, Antonio Signorini, Luigi Fantappie
Similar People  Ulisse Dini, Enrico Betti, Guido Fubini, Mauro Picone, Tullio Levi‑Civita

Doctoral advisor  Enrico Betti, Ulisse Dini

Dash s of old town luigi bianchi mantova autumn winter 2016 2017

Luigi Bianchi (18 January 1856 – 6 June 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.


Luigi Bianchi Luigi Bianchi Wikipedia

Luigi bianchi mantova sartoria fall winter 2015 2016 collection


Luigi Bianchi httpsuploadwikimediaorgwikipediacommons55

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 (sufficiently symmetric) 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 (possibly nonisotropic) 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. (They are essential for understanding the Einstein field equation.) 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.


  • Bianchi, Luigi (1894, 1902, 1909). Lezioni di geometria differenziale (three volumes). Pisa: E. Spoerri.  help)
  • Bianchi: Vorlesungen über Differentialgeometrie, Leipzig 1899
  • Lezioni sulla teoria dei gruppi di sostituzioni e delle equazioni algebriche secondo Galois, Pisa 1899
  • Lezioni sulla teoria delle funzioni di variabile complessa e delle funzioni ellittiche 1916
  • Bianchi, Luigi (1918). Lezioni sulla teoria dei gruppi continui finiti di trasformazioni. Pisa: E. Spoerri. OCLC 4383253. 
  • Lezioni sulla teoria dei numeri algebrici e principi d'aritmetica analitica, 1921
  • References

    Luigi Bianchi Wikipedia

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