Eugenio Beltrami

Eugenio Beltrami ( born November 16, 1835 in Cremona, † February 18, 1900 in Rome) was an Italian mathematician.

Beltrami was a pupil of Enrico Betti, Francesco Brioschi and Luigi Cremona, and gained his title in 1856 as a railroad engineer at the University of Pavia. After a short work as a railway secretary in Verona and Milan, he took a scientific career by staying at the astronomical observatory in Brera again. In 1862 he published his first work in 1864 and professor in Pisa. Further stations of his work were Professor Bologna, Rome, Pavia, and then again Rome. In 1898 he was elected president of the prestigious Accademia dei Lincei.

Beltrami has in the first half of his scientific life totally dedicated to differential geometry and thereby made ​​important contributions. In his Ricerche di analisi applicata alla Geometria there is first a closed description of remaining unchanged in the bending of a surface " absolute functions". Carl Friedrich Gauss was here the first evidence with its curvature. This work initiated the later development of topology. Julius Weingarten described the absolute functions later as " Biegungsinvarianten ".

In 1868, he was tied to a specific model of a non-Euclidean geometry. This model is based on a so-called pseudo- sphere, ie a saddle surface of constant Gaussian curvature. A pseudo- sphere is created by rotating a tractrix about its asymptote.

In the second half of his work Beltrami worked in the field of mathematical physics, in optics, thermodynamics, theory of elasticity, potential theory and electromagnetism. He paid particular attention to the possible reformulation of fundamental laws of physics for spaces with negative curvature, and formulated inter alia, a generalized version of the Laplace operator. The Beltrami equation is of fundamental importance in the theory of quasi -conformal mappings. The complex dilatation is there referred to as Beltrami coefficient.