Generalized $\beta$-conformal change and special Finsler spaces

TL;DR

This paper explores how a generalized $eta$-conformal change affects various special Finsler spaces, analyzes the transformation of the T-tensor, and establishes conditions for projectiveness and geometric properties.

Contribution

It introduces the concept of a generalized $eta$-conformal change in Finsler geometry and studies its effects on special Finsler spaces and tensor transformations.

Findings

Transformation formulas for the T-tensor under the change

Conditions for the change to be projective

Implications of the b-condition on Finsler spaces

Abstract

In this paper, we investigate the change of Finslr metrics $$L(x,y) \to\bar{L}(x,y) = f(e^{\sigma(x)}L(x,y),\beta(x,y)),$$ which we refer to as a generalized $\beta$-conformal change. Under this change, we study some special Finsler spaces, namely, quasi C-reducible, semi C-reducible, C-reducible, $C_2$-like, $S_3$-like and $S_4$-like Finsler spaces. We also obtain the transformation of the T-tensor under this change and study some interesting special cases. We then impose a certain condition on the generalized $\beta$-conformal change, which we call the b-condition, and investigate the geometric consequences of such condition. Finally, we give the conditions under which a generalized $\beta$-conformal change is projective and generalize some known results in the literature.