User:Ema--or/Italian school of differential geometry

The Italian school of differential geometry was a loose association of Italian mathematicians active in the late nineteenth and early 20th century in the closely related mathematical subjects of differential geometry and tensor analysis. Notable members include Beltrami, Ricci-Cubastro, Levi-Civita and Bianchi. Their work was mostly contemporary with the more famed (and much larger) Italian school of algebraic geometry, to which some of them also had close ties to, were influenced by, or were even considered members of, such as Ricci and Beltrami.

Beltrami's work influenced that of Ricci, who in turn created the "Absolute Differential Calculus" with his student Levi-Civta. Other Italians active in the field around this time were Burali-Forte, Marcolongo, Codazzi and Fubini. Vector calculus (today largely subsumed by tensor calculus) due to the efforts of the former, was known for a time in some circles as Italian notation.

The work of the Italians was built largely on Riemann's theories and ran parallel to the efforts of other important differential geometers such as Darboux and later Elie Cartan in France; Grassmann, Weingarten, Killing and Christoffel of Germany, the Norwegian Lie and British Clifford.

It was this group (along with the theories of Riemann) than most directly influenced the early work of Einstein and Grossman in general relativity and subsequently tensor analysis. Einstein later corresponded, even became good friends with Levi-Civita.