Abstract: The significance of this research lies in the generalization of curvature tensors, particularly the concircular curvature tensor, which is studied as a fifth recurrent tensor within the framework of Cartan’s fourth curvature tensor. It contributes to the fundamental understanding of geometric properties in Finsler spaces. This paper builds upon the new concircular curvature tensor $$ M_{ijkh} $$ in generalized fifth recurrent Finsler space, where Cartan's fourth curvature tensor $$ K^{i}_{jkh} $$ is considered in the sense of Berwald $$ GBK\text{-}5RF_{n} $$ via Lie derivative. We obtain the relation between the concircular curvature tensor $$ M_{ijkh} $$ the conformal curvature tensor $$ C_{ijkh} $$ the conharmonic curvature tensor $$ L^{r}_{ikh} $$ and the associate curvature tensor $$ R_{ijkh} $$ if the metric tensor satisfies $$ g_{rj}=1 $$ by Lie derivative. Also, we show that these curvature tensors have the same extension and direction. In addition, the concircular curvature tensor $$ M_{ijkh} $$ and the conharmonic curvature tensor $$ L^{i}_{jkh} $$ are co-directional. We prove that the concircular curvature tensor $$ M_{ijkh} $$ behaves as a fifth recurrent tensor by Lie derivative in the main space.

Keywords: Concircular curvature tensor $$M_{ijkh}$$, Conformal curvature tensor $$C_{ijkh}$$, Conharmonic curvature tensor $$L^{i}_{jkh}$$, Lie-derivative $$\mathcal{L}_{v}$$, $$GBK\text{-}5RF_{n}$$

Pages: 802-806