Expansion of Curvature Tensors under the Berwald Covariant Derivative in Finsler Spaces

Abstract

Curvature tensors are fundamental tools in differential geometry for describing the geometric structure of manifolds. In this paper, we study the expansion of several curvature tensors in Finsler spaces under the Berwald covariant derivative. Various curvature tensors, including the Riemannian, projective, conformal, conharmonic, concircular, and -curvature tensors, are expressed in terms of the Weyl projective curvature tensor. A generalized expansion formula is derived, and a number of identities and theorems concerning the Berwald covariant derivatives of these curvature tensors are established. The obtained results extend classical relations from Riemannian geometry to the Finslerian setting and contribute to the study of curvature structures in Finsler manifolds.