Killing Correspondence in Finsler Spaces

TL;DR

This paper investigates how Killing vector fields correspond between original Finsler spaces and those with a $eta$-change of metric, establishing conditions for such correspondence and exploring related implications.

Contribution

It provides necessary and sufficient conditions for a vector field to be Killing in both original and $eta$-changed Finsler spaces, advancing understanding of metric transformations.

Findings

Derived conditions for Killing vector fields under $eta$-change

Established equivalence criteria for Killing in original and transformed spaces

Discussed implications of Killing correspondence in Finsler geometry

Abstract

The present paper deals with the Killing correspondence between some Finsler spaces. We consider a Finsler space equipped with a $\beta$-change of metric and study the Killing correspondence between the original Finsler space and the Finsler space equipped with $\beta$-change of metric. We obtain necessary and sufficient condition for a vector field Killing in the original Finsler space to be Killing in the Finsler space equipped with $\beta$-change of metric. Certain consequences of such result are also discussed.