In mathematics, Ricci calculus constitutes the rules of index notation and manipulation for tensors and tensor fields on a differentiable manifold, with or without a metric tensor or connection. Wikipedia

Tensor index notation for tensor-based calculations Wikidata

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. Wiktionary

Tensor calculus. Wiktionary (translation)