HIGHER-ORDER CARTAN DERIVATIVES AND CURVATURE TENSOR DECOMPOSITION IN FINSLER SPACES: INSIGHTS INTO MATHEMATICAL AND PHYSICAL APPLICATIONS

This paper delves into the intricate structure of curvature tensors within the realm of Finsler geometry. By harnessing the power of higher-order Cartan derivatives, we introduce a novel decomposition scheme for curvature tensors. This innovative approach not only provides deeper insights into the geometric properties of Finsler spaces but also establishes a foundational framework for further investigations. Our findings reveal that the proposed decomposition is instrumental in unraveling the connections between curvature, torsion, and the underlying metric structure. Moreover, we demonstrate the applicability of our results to various subdomains of Finsler geometry, including Finsler information geometry and Finsler cosmology.