**Luigi Bianchi** made important contributions to differential geometry.

- Saverio Bianchi had studied law at the University of Parma, graduating in July 1848.
- Luigi, however, was attracted to mathematics and he took the competitive entrance examinations for the Scuola Normale Superiore of Pisa in November 1873.
- At the University of Pisa, Luigi Bianchi studied under Enrico Betti and Ulisse Dini and graduated with the highest distinction from Pisa on 30 November 1877.
- After his return to Italy in 1881, Bianchi was appointed to a professorship at the Scuola Normale Superiore at Pisa.
- Luigi Bianchi made important contributions to differential geometry.
- Bianchi also turns to non-Euclidean geometry, taking up the ideas of Beltrami; the surfaces of curvature zero in such geometry draw his special attention.
- Bianchi partial differential equations play an important role.
- The principal fame of Darboux and Bianchi lies in their beautiful textbooks, in which they combine their on results with those of their predecessors.
- Bianchi's 'Lezioni di geometria differenziale' Ⓣ(Lectures on differential geometry) (1893), a new edition of autographed lectures published in 1886, is a systematic treatise of the theory of curves and surfaces, with special attention paid to more-dimensional geometry.
- Perhaps Bianchi's most famous paper was the 92-page On the three-dimensional spaces which admit a continuous group of motions published in 1897.
- As preparation for the general solution, the author applies the Lie-Killing methods for finding all three-dimensional spaces in which the motions of figures with given degrees of freedom are possible - this is enough to outline the goal and the general train of thought of Bianchi's work.
- The importance of his results is known to every reader who is familiar with the awards of the Royal Jablonowski Society for 1901; their citation states that the strength of the methods and the elegance of the solutions need not be pointed out when we are talking about a paper whose author is Bianchi.
- During his time as editor other mathematicians who shared the editorial duties with him include Luigi Cremona, Ulisse Dini, Corrado Segre, Salvatore Pincherle, Tullio Levi-Civita and Francesco Severi.
- Bianchi received many honours including being made a corresponding member of the Accademia dei Lincei in 1887 and a fellow of the Academy in 1893.

Born 18 January 1856, Parma (now Italy). Died 6 June 1928, Pisa, Italy.

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Origin Italy, Physics

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive