On a Generalized \(B_mU\) – Trirecurrent Finsler Space

Abstract

A Finsler space \(F_{n}\) for which the h(v) - curvature tensor \(U_{jkh}^{i}\) satisfies the condition \(B_{m} U_{jkh}^{i}\)=\(λ_{m} U_{jkh}^{i}+μ_{m} (δ_{j}^{i} g_{kh}+δ_{k}^{i} g_{jh} )\), where \(λ_{m}\) and \(μ_{m}\) are non-zero covariant vector fields and \(B_{m}\) is covariant derivative of first order in the sense of Berwald (Berwald’s covariant differential operator). In the present paper, satisfying this condition will be called a generalized \(B_{m} U\)-recurrent space. The tensor \(G_{rkh}^{r}\), the h(v)-torsion tensor \(U_{kh}^{i}\), the G- Ricci tensor \(G_{jk}\) and the U- Ricci tensor \(U_{jk}\) are non-vanishing. Under certain conditions, a generalized \(B_{m} U\) - recurrent space becomes a generalized recurrent tensor. Also, we discuss the decomposing of the h(v) - curvature tensor \(U_{jkh}^{i}\) in Finsler space.