Certain Identities of the Lie - derivative of Tensors in Generalized BK-Fifth Recurrent Finsler Space
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Abstract
This study employs advanced tensor calculus techniques to investigate the properties of the tensorial derivative in generalized fifth-order recurrent Finsler spaces. By systematically analyzing the underlying geometric structure, we derive identities that provide new insights into the relationships between various tonsorial quantities. Our results demonstrate the effectiveness of these techniques in exploring complex geometric structures. This paper introduces a new identity connecting the tensors in generalized fifth recurrence Finsler space for Cartan's fourth curvature tensor in the sense of Berwald by using Lie-derivative. We prove that the Lie - derivative and the Berwald covariant derivative of the fifth order for some curvature and torsion tensors are commutative under certain conditions. We have shown the Lie - derivative for some tensors behave as fifth recurrent and we obtain various identities on Lie - derivative in .
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