Study On Generalized BK-5th Recurrent Finsler Space
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Abstract
Abstract. In this paper, we present a novel new class and investigate the connection between the K-projective curvature tensor and other tensors of Finsler space , this space is characterized by the property for Cartan’s 4th curvature tensor satisfies the certain relationship with the given covariant vectors field, we define this space as a generalized - recurrent space and denote it briefly by - . This paper aims to derive the fifth-order Berwald covariant derivatives of the torsion tensor and the deviation tensor . Additionally, it demonstrates that the curvature vector , the curvature vector , and the curvature scalar are all non-vanishing within the considered space. We have identified tensors that exhibit self-similarity under specific conditions. Furthermore, we have established the necessary and sufficient conditions for certain tensors in this space to have equal fifth-order Berwald covariant derivatives with their lower-order counterparts.
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