Killing Correspondence in Finsler Spaces

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.