Cartan Connection for h-Matsumoto change

Abstract

In the present paper, we have studied the Matsumoto change $\overline{L}(x,y)=\frac{L^2(x,y)}{L(x,y)-\beta (x,y)}$ with an \textsl{h-}vector $b_i(x,y)$. We have derived some fundamental tensors for this transformation. We have also obtained the necessary and sufficient condition for which the Cartan connection coefficients for both the spaces $F^n=(M^n,L)$ and ${\overline{F}}^n=(M^n,\overline{L})$ are same.