ANALYZING THE M-PROJECTIVE CURVATURE TENSOR IN 𝑮𝓑𝑲−𝟓𝑹𝑭𝒏 WITH LIE DERIVATIVE METHODS

In this paper, we investigate the M-projective curvature tensor 𝑊̅𝑗𝑘𝑖 ℎ in generalized fifth recurrence Finsler space for Cartan's fourth curvature tensor in sense of Berwald by using 𝐿𝑖𝑒-derivative. Our study aims to provide new insights into the geometric properties of these spaces and the behavior of the M-projective curvature tensor 𝑊̅𝑗𝑘𝑖 ℎ under Lie differentiation. By employing the Lie derivative, we are able to derive new identities and relations involving the M-projective curvature tensor 𝑊̅𝑗𝑘𝑖 ℎ . We get relationships between some tensors when the M-projective curvature tensor 𝑊̅𝑗𝑘𝑖 ℎ is collineation along a vector field 𝑣(𝑥). Furthermore, we obtain the Berwald covariant derivative of fifth order for some tensors are vanishing and we establish various identities on 𝐿𝑖𝑒-derivative in 𝐺ℬ𝐾 − 5𝑅𝐹𝑛.