Special Finsler spaces admitting a semi-concurrent vector field

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.