On generalized Trirecurrent space by using Gh- Covariant derivative in Finsler geometry

Abstract

This paper investigates generalized U_(|h)-Trirecurrent space within the framework of Finsler geometry, where the curvature tensor satisfies specific birecurrent properties. We derive the condition for a space to be classified as a generalized U_(|h)-Trirecurrent space and introduce related curvature tensors and covariant derivatives. The study includes essential identities satisfied by these tensors and their implications in the context of Finsler spaces with Cartan's second kind covariant derivatives. We also examine necessary and sufficient conditions for certain tensors to be classified as generalized trirecurrent tensors. Several theorems are established, providing detailed relationships between the generalized curvature tensors, torsion, and the covariant derivatives of third order. This paper aims to extend the understanding of curvature structures in Finsler spaces and their geometrical significance.