English Dictionary

Ricci calculus

名詞

(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.

日本語の意味

テンソルやテンソル場を定義し、それらを操作する規則を添字記法で記述する形式体系。リッチ＝キュルバストロが発展させたテンソル解析の理論で、現代数学や物理学の基礎となる。

In differential geometry, the Ricci calculus provides a concise notation for manipulating tensors on curved manifolds.

微分幾何学では、添字記法を用いるテンソル計算が曲がった多様体上のテンソルを操作するための簡潔な記法を提供する。

意味（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.

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.