Deviation equations in spaces with affine connection

TL;DR

This paper explores the relationship between Lie derivatives and deviation equations in spaces with affine connections, deriving equations for both geodesic and non-geodesic trajectories under specific conditions.

Contribution

It introduces a novel approach linking Lie derivatives to deviation equations in affine connection spaces, extending previous work to non-geodesic trajectories.

Findings

Derived deviation equations for geodesic trajectories.

Extended deviation equations to non-geodesic trajectories.

Established conditions on Lie derivatives for these derivations.

Abstract

Connections between Lie derivatives and the deviation equation has been investigated in spaces with affine connection. The deviation equations of the geodesics as well as deviation equations of non-geodesics trajectories have been obtained on this base. This is done via imposing certain conditions on the Lie derivatives with respect to the tangential vector of the basic trajectory.