Luigi Bianchi was educated at a school in Parma, then at the Scuola Normale Superiore before undertaking university studies at the Pisa. He studied under Betti and Dini and graduated with the highest distinction from Pisa in 1877. He completed a doctoral dissertation on applicable surfaces. His research was undertaken at a number of universities throughout Europe, first at Pisa, then at Monaco and finally at Göttingen where he studied with Klein.
After his return to Italy in 1881, Bianchi was appointed to a professorship at the Scuola Normale Superiore of Pisa. He was promoted a number of times, to extraordinary professor in differential geometry, then extraordinary professor in projective geometry, then of analytic geometry. He became a full professor of analytic geometry in 1890.
Bianchi made important contributions to differential geometry. He discovered all the geometries of Riemann that allow a continuous group of transformations. His work on non-euclidean geometries was used by Einstein in his general theory of relativity. His mathematical contributions are described by Hilton in  as follows:-
The greater part of [his early] work is on the properties of surfaces. His methods were based on the theory of the two fundamental differential quadratic forms of Gauss. ... he never published anything which did not contain a real contribution to knowledge. Other subjects which attracted him at time were Lie's theory of continuous groups and the theory of groups of substitutions of the type x' = (ax+b)/(cx+d). But even while he was writing on these topics, papers on surfaces were still appearing, and differential geometry absorbed nearly all his attention for the last twelve years or so of his life.Bianchi wrote a number of influential treatises which :-
... show him to be not only a scientific genius but also a master of clear and attractive style.In particular he wrote Lectures on differential geometry (1894), Lectures on the theory of groups of substitutions (1900), Lectures on the theory of continuous groups (1918), Lectures on the theory of functions of a complex variable (1901) and Lectures on the theory of algebraic numbers (1923).
We should also mention his editorial duties as an editor of Annali di Matematica pura ed applicata. During his time as editor other mathematicians who shared the editorial duties with him include Cremona, Dini, Corrado Segre, Pincherle, Levi-Civita and Severi.
Bianchi received many honours including being made a fellow of the R Accademia dei Lincei in 1893. He was elected an honorary member of the London Mathematical Society and he was similarly honoured by many other Societies.
References (5 books/articles)
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