On Generalized R\(^h\)-Fourrecurrent Finsler Space

Abstract

In this paper, we introduce a Finsler space which Cartan's third curvature tensor R_{jkh}^i satisfies the generalized four recurrent property in sense of Cartan's, this space characterized by the following condition \(R_{jkh׀l׀m׀n׀s}^i =  u_{lmns} R_{jkh}^i + v_{lmns} (δ_k^i g_{jh} - δ_h^i g_{jk}), R_{jkh}^i≠ 0\), where ׀l׀m׀n׀s is h- covariant derivative of fourth order (Cartan's second kind covariant differential operator), with respect x\(^l\), x\(^m\), x\(^n\) and x\(^s\), respectively, where u_{lmns} and v\(_{lmns}\) are non-zero covariant tensor fields of fourth order called recurrence tensor fields, is introduced, such space is called as a generalized R^h- fourrecurrent Finsler space and we denote by GR\(^h\)- FR- F\(_n\) and we obtained some generalized fourrecurrent in this space.