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

Authors

  • Adel Mohammed Ali Al-Qashbari Dept. of Math's., Faculty of Educ. Aden, Univ. of Aden, Aden, Yemen
  • Fahmi Ahmed Mothana Al-ssallal Dept. of Math's., Faculty of Educ. Aden, Univ. of Aden, Aden, Yemen

DOI:

https://doi.org/10.47372/ejua-ba.2025.2.449

Keywords:

Finsler space, Cartan’s covariant derivative expansion, Curvature tensor, Identities, Geometric properties

Abstract

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.

Downloads

Download data is not yet available.

Author Biography

Adel Mohammed Ali Al-Qashbari, Dept. of Math's., Faculty of Educ. Aden, Univ. of Aden, Aden, Yemen

Dept. of Med. Eng.‚ Faculty of the Engineering and Computers, Univ. of Science & Technology, Aden‚ Yemen

Published

2025-06-30

How to Cite

Al-Qashbari, A. M. A. ., & Al-ssallal, F. A. M. . (2025). HIGHER-ORDER CARTAN DERIVATIVES AND CURVATURE TENSOR DECOMPOSITION IN FINSLER SPACES: INSIGHTS INTO MATHEMATICAL AND PHYSICAL APPLICATIONS. Electronic Journal of University of Aden for Basic and Applied Sciences, 6(2), 141–151. https://doi.org/10.47372/ejua-ba.2025.2.449