On certain a generalized \(N_{|m}\) ̶ Recurrent Finsler space

Abstract

A Finsler space \(F_n\) for which the normal projective curvature tensor \(N_{jkh}^i\) satisfies \(N_{jkh|m}^i = λ_m N_{jkh}^i + μ_m (δ_h^i g_{jk} - δ_k^i g_{jh} ), N_{jkh}^i ≠ 0\), where \(λ_m\) and \(μ_m\) are non-zero covariant vectors field, will be called a generalized \(N_{|m}\) ̶ recurrent space. The curvature vector \(H_k\), the curvature scalarH and Ricci tensor \(N_{jk}\) are non-vanishing. When the generalized \(N_{|m}\) ̶ recurrent space is affinely connected space and under certain conditions, we obtain various results. Also, in generalized \(N_{|m}\) ̶ recurrent space, Weyl's projective curvature tensoris a generalized recurrent tensor.