Berwald Covariant Derivative and Lie Derivative of Conharmonic Curvature Tensors in Generalized Fifth Recurrent Finsler Space
Abstract
This paper builds upon new define for the conharmonice curvature tensor in generaralized fifth recurrent Finsler space that Cartan’s fourth curvature tensor in sense of Berwald - via Lie derivative. We define a new conharmonic curvature tensor and explore its relationships with other established curvature tensors. Through various mathematical operations, including the Berwald covariant derivative and the Lie derivative, we derive new expressions for the conharmonic tensor and its interactions with other curvature tensors. The main results include the commutativity of the Berwald covariant derivative of the fifth order with the Lie derivative, as well as the distributivity of the Lie derivative over the addition of curvature tensors. Additionally, we establish several theorems and corollaries that enhance the understanding of the behavior of curvature tensors in
GBK-5RFn.
Subject Classification: 53B40, 53C60, 53C25.
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