On Invariant Operations on a Manifold with a Linear Connection and an Orientation

Adrián Gordillo-Merino, Raúl Martínez-Bohórquez and José Navarro-Garmendia
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Adrián Gordillo-Merino: Departamento de Matemáticas, Universidad de Extremadura, Avenida de Elvas s/n, 06006 Badajoz, Spain
Raúl Martínez-Bohórquez: Departamento de Matemáticas, Universidad de Extremadura, Avenida de Elvas s/n, 06006 Badajoz, Spain
José Navarro-Garmendia: Departamento de Matemáticas, Universidad de Extremadura, Avenida de Elvas s/n, 06006 Badajoz, Spain

Mathematics, 2021, vol. 9, issue 20, 1-18

Abstract: We prove a theorem that describes all possible tensor-valued natural operations in the presence of a linear connection and an orientation in terms of certain linear representations of the special linear group. As an application of this result, we prove a characterization of the torsion and curvature operators as the only natural operators that satisfy the Bianchi identities.

Keywords: natural tensors; linear connections; torsion tensor; curvature operator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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