Generalized H^h-Recurrent Finsler Spaces and Their Relations with Berwald and Cartan Curvature Tensors

Abstract

This paper studies generalized recurrence in Finsler geometry with emphasis on the Berwald and Cartan curvature tensors. Finsler spaces extend Riemannian geometry by allowing geometric quantities to depend on both position and direction. The research introduces generalized recurrence conditions for these curvature tensors and develops theoretical relations describing their behavior. A new concept, called generalized -recurrent Finsler spaces, is proposed and analyzed. The study defines these spaces through recurrence relations involving covariant vector fields, curvature tensors, and deviation tensors. Several theorems are established to characterize the recurrence properties of the Berwald tensor . The results classify Finsler spaces according to the degree and type of recurrence. The obtained relations reveal structural connections between Berwald and Cartan tensors under generalized recurrence conditions. These findings contribute to understanding curvature structures and symmetry properties in non-Riemannian geometry. The study also extends the theoretical framework of recurrence in differential geometry and its applications in Finsler spaces.