Geometric Properties and Recurrence Conditions in Generalized H^v-Recurrent Finsler Spaces with Applications to Differential Geometric Modelling

Abstract

This paper investigates the geometric structure and recurrence properties of generalized -recurrent Finsler spaces - , characterized by a Berwald curvature tensor  satisfying a specific (v)-covariant recurrence condition. Several fundamental identities are derived for the first-order (v)-covariant derivatives of the Berwald curvature tensor, the deviation tensor, the Ricci tensor, the curvature vector, and the associated torsion and curvature tensors. Necessary and sufficient conditions for these tensors to be generalized recurrent are established through detailed analysis using Cartan’s first and second kind covariant differential operators. The results show that the Berwald Ricci tensor and the Berwald scalar curvature cannot vanish in such spaces, and that several geometric objects exhibit strict recurrence behavior governed by the recurrence vectors  and . Furthermore, generalized recurrence conditions for Izumi’s tensor  are obtained, along with new identities linking various torsion and curvature components. The theoretical framework developed in this study provides deeper insight into the structure of Finsler spaces with generalized recurrence and supports potential applications in engineering fields that rely on differential geometric modelling, such as nonlinear mechanical systems, anisotropic material modelling, and advanced control systems.