Transports along Paths in Fibre Bundles. III. Consistency with Bundle Morphisms

TL;DR

This paper investigates the conditions under which transports along paths in fibre bundles are consistent with bundle morphisms, including special cases like vector bundles with Hermitian structures, advancing the theoretical understanding of fibre bundle transports.

Contribution

It formulates the general problem of transport-morphism consistency in fibre bundles and explores specific cases such as vector bundles with Hermitian structures.

Findings

Established criteria for transport and morphism consistency in fibre bundles.

Analyzed the special case of linear transports in vector bundles with Hermitian structures.

Provided theoretical insights into the compatibility conditions for transports and bundle morphisms.

Abstract

The general problem for consistency between arbitrary transports along paths in fibre bundles and bundle morphisms between them is formulated and investigated. The special case of one fibre bundle, its morphism and transport along paths acting in it is considered. The consistency between linear transports along paths in a vector bundle and a Hermitian structure in it is studied.