Abstract

In this paper, we defined a Finsler space whose Berwald curvature tensor \(H_{jkh}^i\) satisfies the condition
\(B_m B_n H_{jkh}^i=  a_{mn} H_{jkh}^i+ b_{mn} (δ_k^i g_{jh}-δ_h^i g_{jk})-2y^r µ_nB_r (δ_k^i C_{jhm}-δ_h^i C_{jkm})\),where B_m B_n are Berwald covariant derivative of second order with respect to x^m and xⁿ, respectively, a_mn and b_mn are non-zero covariant tensors field. The purpose of this paper is to develop the generalized βH-birecurrent space by studying some properties of generalized βH-birecurrent affinely connected space, P2-like generalized βH-birecurrent space and P^*-generalized βH-birecurrent space. Some theorems and conditions have been pointed out which reduce a generalized βH-birecurrentaffinely connected space F_n (n>2) into a Finsler space of curvature scalar.