Differential Properties of the Conformal Curvature Tensor in Fifth-Recurrent Finsler Space: A Lie and Berwald Approach

Adel M. Al-Qashbari; Alaa A. Abdallah; Saeedah M. Baleedi

doi:10.5281/zenodo.20558308

Adel M. Al-Qashbari Department of Engineering, Faculty of Engineering & Computing University of Science and Technology, Aden, Yemen
Alaa A. Abdallah Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad 431004, India
Saeedah M. Baleedi Department of Mathematics, Education Faculty - Zinjibar, Abyan University, Abyan,Yemen

DOI: https://doi.org/10.5281/zenodo.20558308

Keywords: Lie-derivative, Conformal curvature tensor, Generalized BK-fifth recurrent Finsler space, Berwald covariant derivative, Finsler geometry, Differential geometry

Abstract

This research investigates the Lie-derivative and Berwald covariant derivatives of the conformal curvature tensor in the generalized fifth recurrent Finsler space. The study focuses on the mathematical properties and interrelations of these tensors, exploring the behavior of the conformal curvature tensor under various differential operators, including the Lie derivatives and Berwald covariant derivatives. This paper builds upon the definition for the conformal curvature tensor under the Lie derivative in generalized BK-fifth recurrent Finsler space. We study the relations between the mentioned curvature tensors and Rᶦⱼₖₕ by Lie-derivative. The Lie-derivative for the conformal curvature tensor Cᵢⱼₖₕ and the fifth-order Berwald covariant derivatives are mutually commutative. In addition, we prove that the conformal curvature tensor Cᵢⱼₖₕ behaves as a fifth recurrent under certain conditions. In conclusion, we demonstrate that applying the fifth-order Berwald covariant derivative to the Lie derivative of the curvature scalar R is vanishing.

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