Special Finsler spaces admitting a semi-concurrent vector field

TL;DR

This paper investigates conditions under which certain special Finsler spaces become Riemannian when admitting a semi-concurrent vector field, establishing equivalences and necessary conditions.

Contribution

It demonstrates that various classes of Finsler spaces are Riemannian if they admit a semi-concurrent vector field and provides conditions for Finsler spaces to become Riemannian under $C$-conformal conditions.

Findings

Quasi-$C$-reducible Finsler spaces are Riemannian with semi-concurrent vector fields.

$C3$-like, $C^{h}$-recurrent, and $P2$-like Finsler spaces are Riemannian under the same conditions.

Necessary and sufficient conditions for $C$-conformal Finsler spaces to be Riemannian.

Abstract

The main objective of this paper is to study semi-concurrent vector fields on a Finsler manifold. We show that the quasi-$C$-reducible Finsler space, $C3$-like Finsler space, $C^{h}$-recurrent Finsler space, and $P2$-like Finsler space are equivalent to Riemannian if they admit a semi-concurrent vector field. Further, we prove the necessary and sufficient condition for a Finsler space satisfying $C$-conformal condition to become Riemannian.