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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Adrián Gordillo-Merino & Raúl Martínez-Bohórquez & José Navarro-Garmendia, 2021. "On Invariant Operations on a Manifold with a Linear Connection and an Orientation," Mathematics, MDPI, vol. 9(20), pages 1-18, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:20:p:2577-:d:655792
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