Some intrinsic properties of h-Randers conformal change

TL;DR

This paper investigates the properties of h-Randers conformal change in Finsler geometry, deriving formulas for geodesic coefficients and conditions under which certain special Finsler spaces retain their properties under this change.

Contribution

It introduces the concept of h-Randers conformal change in Finsler metrics and analyzes its effects on various special Finsler spaces and their geometric properties.

Findings

Derived expressions for geodesic spray coefficients under h-Randers conformal change.

Identified conditions for preserving Berwald and Landsberg space properties.

Studied the impact on quasi-C-reducible, C-reducible, S3-like, and S4-like Finsler spaces.

Abstract

In the present paper we have considered h-Randers conformal change of a Finsler metric $ L $, which is defined as \begin{center}$ L(x,y)\rightarrow \bar{L}(x, y)=e^{\sigma(x)}L(x, y)+\beta (x, y), \end{center} where $ \sigma(x) $ is a function of x, $\beta(x, y) = b_{i}(x, y)y^{i}$ is a 1- form on $M^{n}$ and $b_{i}$ satisfies the condition of being an h-vector. We have obtained the expressions for geodesic spray coefficients under this change. Further we have studied some special Finsler spaces namely quasi-C-reducible, C-reducible, S3-like and S4-like Finsler spaces arising from this metric. We have also obtained the condition under which this change of metric leads a Berwald (or a Landsberg) space into a space of the same kind.