Generalized $\beta$-conformal change of Finsler metrics

TL;DR

This paper introduces a broad transformation of Finsler metrics called the generalized β-conformal change, unifying various existing metric changes and analyzing their effects on geometric structures and invariants.

Contribution

It defines and studies a new generalized β-conformal change of Finsler metrics, encompassing many known transformations and exploring their geometric implications.

Findings

Derived transformation formulas for Finsler connections.

Identified invariants under the generalized β-conformal change.

Unified various special Finsler space transformations as cases.

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.