Geometric Analysis of Lie and Berwald Derivatives of Inheritance Tensors in Finsler Spaces

This paper introduces the concept of P-curvature inheritance in generalized recurrent Finsler spaces and establishes various types of curvature inheritance tensors in such spaces. We prove that the fundamental function of the Finsler space is given by F=yiyrδrkgikn. Moreover, we infer that the Lie derivative of the curvature scalar R is equal to the Lie derivative of the curvature scalar K, and the Lie derivative of the recurrence vector field μm vanishes. Additionally, we establish new mathematical formulas for the scalar function α(x) and the scalar form of the metric tensor gij that admit P-curvature inheritance. A tensor (δlkPkhi) and the R-Ricci tensor possess an inheritance property in the generalized BP-recurrent Finsler space. In the same vein, we obtain conditions under which the Lie derivative and the Berwald covariant derivative of the curvature scalar P commute. Finally, we provide practical examples that illustrate the understanding of the obtained results.