Some Types of Generalized $H^h$-Recurrent in Finsler Spaces

Abstract

The purpose of this paper is to develop some properties of generalized $H^{h}$-recurrent affinely connected space, P2-like generalized $H^{h}$-recurrent space and $P^{\ast}$-generalized $H^{h}$-recurrent space for Berwald curvature tensor $H_{jkh}^{i}$ which satisfies the condition $H_{jkh\vert l}^{i}=\lambda_{l}H_{jkh}^{i}+\mu_{l}(\delta _{h}^{i} g_{jk}-\delta_{k}^{i} g_{jh})$, where $\vert l$ is h-covariant differentiation, $\lambda_{l}$ and $\mu_{l}$ are non-null covariant vectors field is introduced and such space is called as a generalized $H^{h}$-recurrent space and denote it briefly by $G H^{h}$-$R F_{n}$. Some theorems and conditions have been pointed out which reduce a generalized $H^{h}$-recurrent space $F_{n}(n>2)$ into a Finsler space of curvature scalar.