Luigi Bianchi (January 18, 1856 - June 6, 1928) was an Italian mathematician. He was born in Parma, Emilia-Romagna, and died on 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. January 18 is the 18th day of the year in the Gregorian calendar. ... 1856 was a leap year starting on Tuesday (see link for calendar). ... June 6 is the 157th day of the year in the Gregorian calendar (158th in leap years), with 1 day remaining // 1508 - Maximilian I, Holy Roman Emperor, is defeated in Friulia by Venetian forces; he is forced to sign a three-year truce and cede several territories to Venice 1513... Year 1928 (MCMXXVIII) was a leap year starting on Sunday (link will display full calendar). ... Country Italy Region Emilia-Romagna Province Parma (PR) Mayor Elvio Ubaldi (since May 28, 2002) Elevation 55 m Area 260 km² Population  - Total (as of December 31, 2004) 175,789  - Density 676/km² Time zone CET, UTC+1 Coordinates Gentilic Parmigiani (Parmensi are called the provinces inhabitants) Dialing code... Emilia-Romagna is one of the 20 Regions of Italy. ... This article discusses the Italian city. ... Alternative meaning: Nineteenth Century (periodical) (18th century — 19th century — 20th century — more centuries) As a means of recording the passage of time, the 19th century was that century which lasted from 1801-1900 in the sense of the Gregorian calendar. ...

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. Gregorio Ricci-Curbastro (January 12, 1853 - August 6, 1925) was an Italian mathematician. ... The Scuola Normale Superiore di Pisa, also known in Italian language as Scuola Normale (English: Normal High School College of Pisa or Normal School), is with no doubt the most elitary college in the whole Italian universities world. ... This article discusses the Italian city. ... Enrico Betti (21 October 1823 - 11 August 1892) was an Italian mathematician, now remembered mostly for his 1871 paper on topology that led to the later naming after him of the Betti numbers. ... In mathematics, differential topology is the field dealing with differentiable functions on differentiable manifolds. ... A Möbius strip, an object with only one surface and one edge; such shapes are an object of study in topology. ... Ulisse Dini (Born November 14, 1845 in Pisa, Italy-Died October 28, 1918 in Pisa, Italy) was a mathematician and politician. ... Complex analysis is the branch of mathematics investigating holomorphic functions, i. ... Bernhard Riemann. ... In mathematics, a Lie group is an analytic real or complex manifold that is also a group such that the group operations multiplication and inversion are analytic maps. ... Marius Sophus Lie (IPA pronunciation: , pronounced Lee) (December 17, 1842 - February 18, 1899) was a Norwegian-born mathematician. ... Felix Christian Klein (April 25, 1849, Düsseldorf, Germany – June 22, 1925, Göttingen) was a German mathematician, known for his work in group theory, function theory, non-Euclidean geometry, and on the connections between geometry and group theory. ... The Scuola Normale Superiore di Pisa, also known in Italian language as Scuola Normale (English: Normal High School College of Pisa or Normal School), is with no doubt the most elitary college in the whole Italian universities world. ... This article discusses the Italian city. ... Gregorio Ricci-Curbastro (January 12, 1853 - August 6, 1925) was an Italian mathematician. ... Guido Fubini (January 19, 1879 - June 6, 1943) was an Italian mathematician, best known for Fubinis theorem. ...

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. In mathematics, the Bianchi classification, named for Luigi Bianchi, is a classification of the 3-dimensional real Lie algebras into 11 classes, 9 of which are single groups and two of which have a continuum of isomorphism classes. ... In mathematics, a Lie group, named after Norwegian mathematician Sophus Lie (IPA pronunciation: , sounds like Lee), is a group which is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure. ... In mathematics, an isometry, isometric isomorphism or congruence mapping is a distance-preserving isomorphism between metric spaces. ... In Riemannian geometry, a Riemannian manifold is a real differentiable manifold in which each tangent space is equipped with an inner product in a manner which varies smoothly from point to point. ... In mathematics, an isomorphism (in Greek isos = equal and morphe = shape) is a kind of mapping between objects, devised by Eilhard Mitscherlich, which shows a relation between two properties or operations. ... In mathematics, a Lie algebra is an algebraic structure whose main use is in studying geometric objects such as Lie groups and differentiable manifolds. ... Marius Sophus Lie (IPA pronunciation: , pronounced Lee) (December 17, 1842 - February 18, 1899) was a Norwegian-born mathematician. ...

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. Luther Pfahler Eisenhart (13 Jan, 1876-28 Oct, 1965) was an American mathematician, best known today for his contributions to semi-Riemannian geometry. ... Abraham Haskel Taub (February 1, 1911–August 9, 1999) was a distinguished American mathematician and physicist, well known for his important contributions to the early development of general relativity, as well as differential geometry and differential equations. ... General relativity (GR) [also called the general theory of relativity (GTR) and general relativity theory (GRT)] is the geometrical theory of gravitation published by Albert Einstein in 1915/16. ... In mathematics, a Bianchi group is a group of the form PSL2(Od) where d is a positive square-free integer. ...

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! In mathematics, specifically differential geometry, the infinitesimal geometry of Riemannian manifolds with dimension at least 3 is too complicated to be described by a single number at a given point. ... In differential geometry, the Riemann curvature tensor is the most standard way to express curvature of Riemannian manifolds, or more generally, any manifold with an affine connection, torsionless or with torsion. ... For other topics related to Einstein see Einstein (disambig) In physics, the Einstein field equation or the Einstein equation is a tensor equation in the theory of gravitation. ... Tullio Levi-Civita. ...

See also

• Bianchi identities
• Bianchi group

In mathematics, specifically differential geometry, the infinitesimal geometry of Riemannian manifolds with dimension at least 3 is too complicated to be described by a single number at a given point. ... In mathematics, a Bianchi group is a group of the form PSL2(Od) where d is a positive square-free integer. ...

External links

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

References

• Bianchi, Luigi (1894, 1902, 1909). Lezioni di geometria differenziale (three volumes). Pisa: E. Spoerri. 
• Bianchi, Luigi (1918). Lezioni sulla teoria dei gruppi continui finiti di trasformazioni. Pisa: E. Spoerri. OCLC 4383253. 
• Hilton, H. (1929). "Luigi Bianchi". J. London Math. Soc. 4: 79–80. 
• O'Connor, J. J.; & Robertson, E. F.. Luigi Bianchi. MacTutor History Archive. Retrieved on July 10, 2005.
• Luigi Bianchi at the Mathematics Genealogy Project