Deviation equations in spaces with a transport along paths

TL;DR

This paper introduces deviation equations in manifolds with transports along paths, extending the classical concept to spaces with general transports, and explores their form when a linear connection is present.

Contribution

It develops deviation equations in manifolds with transports along paths and analyzes their form in spaces with linear connections, generalizing existing deviation concepts.

Findings

Deviation equations are formulated in spaces with transports along paths.

The form of deviation equations is analyzed in spaces with linear connections.

The work extends classical deviation equations to more general geometric settings.

Abstract

The displacement and deviation vectors in spaces (manifolds), the tangent bundle of which is endowed with a transport along paths, are introduced. In case these spaces are equipped with a linear connection, the deviation equations (between arbitrary, geodesic or not, paths) in such spaces are investigated.