Ricci calculus

Ricci calculus

English

Etymology

Named after Gregorio Ricci-Curbastro, who developed the notation and theory in the late 19th century.

Noun

Ricci calculus

1. (mathematics) 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.
   • 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.

   • 1986, Warner Allen Miller, Geometric Computation: Null-Strut Geometrodynamics and the Inchworm Algorithm, Joan M. Centrella (editor), Dynamical Spacetimes and Numerical Relativity, Cambridge University Press, page 256,

     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.

   • 1995, Ignazio Ciufolini, John Archibald Wheeler, John Wheeler, Gravitation and Inertia, Princeton University Press, page 19,

     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.

Synonyms

• (tensor calculus): absolute differential calculus, tensor analysis, tensor calculus

Related terms

• Ricci decomposition

Translations

tensor calculus

Italian: calcolo tensoriale m

Further reading

• Tensor (intrinsic definition) on Wikipedia.Wikipedia
• Abstract index notation on Wikipedia.Wikipedia
• Penrose graphical notation on Wikipedia.Wikipedia
• Regge calculus on Wikipedia.Wikipedia