On \(W_{jkh}^{i}\) in Generalized \(\beta P -\) Recurrent and Birecurrent Finsler Space

Finsler geometry is a kind of differential geometry. It usually considers as a generalization of Riemannian geometry. It has many applications in various fields of Physics such as the theory of relativity. The generalized recurrence and birecurrence property in Finsler space have been discussed by the Finslerian geometrics. The aim of this paper is to study the relationship between Wely’s projective curvature tensor \(W_{jkh}^{i}\) and Cartan's secend curvature tensor \(P_{jkh}^{i}\) in generalized recurrent and birecurrent space. Additionally, we find the condition for the curvature tensor \(W_{jkh}^{i}\) that is generalized recurrent and birecurrent tensor. Further, diverse theorems have been established and proved.