Finsler space subjected to a Kropina change with an h-vector

Abstract

In this paper, we discuss the Finsler spaces $(M^n,L)$ and $(M^n,{}^{\ast }L)$, where ${}^{\ast }L(x,y)$ is obtained from $L(x,y)$ by Kropina change ${}^{\ast }L(x,y)=\frac{L^2(x,y)}{b_i(x,y)y^i}$ and $b_i^{}(x,y)$ is an $h$-vector in $(M^n,L)$. We find the necessary and sufficient condition when the Cartan connection coefficients for both spaces $(M^n,L)$ and $(M^n,{}^{\ast }L)$ are the same. We also find the necessary and sufficient condition for Kropina change with an $h$-vector to be projective.