ON THE LIE DERIVATIVE OF CURVATURE TENSORS AND THEIR RELATIONS IN $GBK- 5RF_n$

Abstract

This paper investigates the behavior of curvature tensors under the Lie derivative. We derive novel relations between various curvature tensors, such as the Riemann curvature tensor, Ricci tensor, and scalar curvature, when subjected to the Lie derivative. Our results provide a deeper understanding of the geometric properties of manifolds and have potential applications in fields such as general relativity and differential geometry. Also, we build upon the definitions for the conformal and conharmonice curvature tensor in generaralized fifth recurrent Finsler space $GBK-5RF_n$. We study the various relations between above curvature tensors and the Cartan’s third curvature tensor R$_{jkh}^i$ by Lie-derivative.