A New Class of Generalized U-Birecurrent Finsler Spaces and Their Curvature Properties

Abstract

In this paper, we introduce a new class of generalized U-birecurrent Finsler spaces defined in terms of second-order Berwald covariant derivatives of the h(v)-curvature tensor. This new structure extends existing concepts of recurrent and birecurrent Finsler spaces by incorporating higher-order differential conditions. Several fundamental properties of the proposed spaces are established, including relationships between the h(v)-curvature tensor and other important curvature tensors such as Cartan’s curvature tensors, Berwald curvature tensor, and the normal projective curvature tensor. Furthermore, a series of theorems and corollaries are derived to characterize the geometric behavior of these spaces under generalized recurrence conditions. The obtained results provide a broader framework for the study of curvature structures in Finsler geometry and contribute to the ongoing development of higher-order geometric analysis.