Conformal change of special Finsler spaces

TL;DR

This paper investigates how various special Finsler spaces behave under conformal changes, providing intrinsic conditions for invariance and examining the effects on related connections and curvature tensors.

Contribution

It offers the first intrinsic criteria for the invariance of numerous special Finsler spaces under conformal transformations and analyzes the impact on associated connections and curvature tensors.

Findings

Necessary and sufficient conditions for invariance under conformal change.

Explicit formulas for conformal change of Chern and Hashiguchi connections.

Analysis of curvature tensor transformations under conformal change.

Abstract

The present paper is a continuation of a foregoing paper [Tensor, N. S., 69 (2008), 155-178]. The main aim is to establish \emph{an intrinsic investigation} of the conformal change of the most important special Finsler spaces, namely, $C^{h}$-recurrent, $C^{v}$-recurrent, $C^{0}$-recurrent, $C_{2}$-like, quasi-$C$-reducible, $C$-reducible, Berwald space, $S^{v}$-recurrent, $P^*$-Finsler manifold, $R_{3}$-like, $P$-symmetric, Finsler manifold of $p$-scalar curvature and Finsler manifold of $s$-$ps$-curvature. Necessary and sufficient conditions for such special Finsler manifolds to be invariant under a conformal change are obtained. Moreover, the conformal change of Chern and Hashiguchi connections, as well as their curvature tensors, are given.