Generalized $\beta$-conformal change of Finsler metrics

Abstract

In this paper, we introduce and investigate a general transformation or change of Finsler metrics, which is referred to as a generalized $\beta$-conformal change: $$L(x,y) \longrightarrow\overline{L}(x,y) = f(e^{\sigma(x)}L(x,y),\beta(x,y)).$$ This transformation combines both $\beta$-change and conformal change in a general setting. The change, under this transformation, of the fundamental Finsler connections, together with their associated geometric objects, are obtained. Some invariants and various special Finsler spaces are investigated under this change. The most important changes of Finsler metrics existing in the literature are deduced from the generalized $\beta$-conformal change as special cases.