Luigi Bianchi was born on January 18 1856 in Parma, Italy, and died on June 6 1928 in Pisa, Italy. He was a leading mathematician 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 algebraic 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 famous 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!

See also

• Bianchi identities
• Bianchi group

External links

• Robert T. Jantzen (Villanova University) offers translations of some of Bianchi's papers, plus a biography of Bianchi.

References

1856 births | 1928 deaths | Natives of Parma | Differential geometers | Italian mathematicians

Luigi Bianchi | Luigi Bianchi