RICCI-CURBASTRO, GREGORIO

born Jan. 12, 1853, Lugo, Papal States died Aug. 6, 1925, Bologna, Italy Italian mathematician instrumental in the development of the absolute differential calculus (also called the Ricci calculus), now known as tensor analysis. Ricci was a professor at the University of Padua from 1880 to 1925. His earliest work was in mathematical physics, notably on the laws of electric circuits and in differential equations. The systematic theory of tensor analysis was created by Ricci from 1887 to 1896, with significant extensions later contributed by his pupil Tullio Levi-Civita. Tensor analysis concerns relations that are covariant; i.e., relations that remain valid when changed from one system of coordinates to any other system. The origins of tensor analysis are rooted in the differential geometry of the noted German mathematician Georg Riemann. The first steps in the development of the appropriate technique of tensors had been taken by Elwin Bruno Christoffel of Germany, while important concepts had been introduced by Eugenio Beltrami of Italy and Rudolf O.S. Lipschitz of Germany. For some time Ricci's new calculus was largely unnoticed. Later, however, Einstein found Ricci's methods to be indispensable as the mathematical formulation of his theory of general relativity. In his studies of applying tensor analysis to the study of surfaces, Ricci encountered several interesting metric properties of hyperspaces. One of them, a form of the Riemann-Christoffel curvature tensor, was the Ricci tensor (Rij), which occurs in Einstein's gravitational equations and is often called the Einstein tensor. The interest in tensor analysis generated by its use in general relativity has resulted in extensive use of it in differential geometry and other branches of mathematics.