A Study of M-Projective Curvature Tensor in Via Lie Derivative
Abstract
In this paper, we investigate the M-projective curvature tensor ?? ??? ? in generalized fifth recurrence Finsler space for Cartan's fourth curvature tensor in sense of Berwald by using ???-derivative. Our study aims to provide new insights into the geometric properties of these spaces and the behavior of the M-projective curvature tensor ?? ??? ? under Lie differentiation. By employing the Lie derivative, we are able to derive new identities and relations involving the M-projective curvature tensor ?? ??? ? . We get relationships between some tensors when the M-projective curvature tensor ?? ??? ? is collineation along a vector field ? ? (?). Furthermore, we obtain the Berwald covariant derivative of fifth order for some tensors are vanishing and we establish various identities on ???-derivative in ??? ? 5???.
Keywords
M-projective curvature tensor ??
???
?
Generalized ?? ?fifth recurrent space
Berwald covariant derivative of fifth order
???-derivative.
References
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