A decomposition analysis of Weyl's curvature tensor via Berwald’s first and second order derivatives in Finsler spaces

This research paper explores the decomposition of Weyl's curvature tensor through the lens of Berwald’s first and second-order derivatives in Finsler spaces. We analyze how Berwald’s differential geometry methods apply to Finsler spaces, which generalize Riemannian geometry and provide a more flexible framework for understanding curvature. The study highlights the importance of these decompositions in advancing both the theoretical aspects of Finsler geometry and their potential applications in physics, particularly in the realm of gravitational theories. Our findings offer a comprehensive understanding of the geometric structures that emerge in Finsler spaces, facilitating further research in high-dimensional and non-Riemannian manifolds.