Commutation Formulae With Respect to Non-Symmetric Affine Connection

TL;DR

This paper derives commutation formulae for covariant derivatives of tensors using non-symmetric affine connections, expanding the mathematical tools available for differential geometry.

Contribution

It introduces new commutation formulae involving covariant derivatives with respect to non-symmetric affine connections, generalizing existing symmetric cases.

Findings

Derived explicit commutation formulae for non-symmetric affine connections.

Extended the framework of covariant derivatives to include non-symmetric cases.

Provided formulas applicable to advanced geometric and physical theories.

Abstract

Commutation formulae with respect to a non-symmetric affine connection are obtained in this paper. The components of commutation formulae in this paper are covariant derivatives of tensors with respect to symmetric and non-symmetric affine connection.