Linear transports along paths in vector bundles V. Properties of curvature and torsion

TL;DR

This paper provides a geometric interpretation of curvature and torsion for linear transports along paths in vector bundles, deriving identities that generalize classical results for linear connections.

Contribution

It introduces a geometric framework for understanding curvature and torsion of linear transports, extending classical identities to a broader context.

Findings

Derived Bianchi-type identities for curvature and torsion.

Unified geometric interpretation encompassing classical linear connection results.

Generalized properties of curvature and torsion in vector bundle transports.

Abstract

A geometric interpretation of curvature and torsion of linear transports along paths is presented. A number of (Bianchi type) identities satisfied by these quantities are derived. The obtained results contain as special cases the corresponding classical ones concerning curvature and torsion of linear connections.