Cartan Connection for h-Matsumoto change

TL;DR

This paper investigates a specific Matsumoto change in Finsler geometry involving an h-vector, deriving fundamental tensors and conditions under which the Cartan connection remains unchanged.

Contribution

It introduces a new Matsumoto change involving an h-vector and establishes conditions for the invariance of the Cartan connection coefficients.

Findings

Derived fundamental tensors for the Matsumoto change with h-vector.

Established necessary and sufficient conditions for Cartan connection invariance.

Analyzed the impact of the change on Finsler space structures.

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.