Meaning of Ricci calculus | Babel Free

Definitions

A formal system in which index notation is used to define tensors and tensor fields and the rules for their manipulation; the theory of tensor calculus as developed by Gregorio Ricci-Curbastro, which formed the foundation of the modern theory.

Equivalents

Examples

“1945 [McGraw-Hill, 2nd Edition], E. T. Bell, The Development of Mathematics, Dover, 1992, page 357, The method of calculation is the absolute differential calculus, or tensor analysis, of M. M. G. Ricci (1853–1925, Italian), which was noted earlier in connection with the general progress of recent mathematics toward structure. The Ricci calculus, however, originated in the algebra of quadratic differential forms. […] The Ricci calculus did not come into its own geometrically until it was publicized by the relativists, when the geometers adopted and further developed it.”

“This structure, we suggest, will show more clearly when examined in the language of geometry rather than in the language of differential equations, more readily in Regge calculus than in Ricci calculus, and more directly from a geometry idealized to be blockwise flat than from functions idealized to be piecewise linear.”

“The absolute differential calculus is also known as tensor calculus or Ricci calculus. Its development was mainly due to Gregorio Ricci Curbastro (1853-1925) who elaborated the theory during the ten years 1887-1S96.”

CEFR level