The Role of the Weyl Projective Curvature Tensor and Its Relation to other Cur-vatures Tensors in Spacetime Geometry

Abstract

This research delves into the intricate realm of Finsler geometry, with a particular focus on curvature tensors. The paper aims to establish novel identities that govern the expansion of these tensors within the broader context of Finsler space. Through rigorous mathematical analysis, we explore the inter relationships between various curvature tensors and their corresponding expansions. The derived identities not only deepen our understanding of the intrinsic geometric properties of Finsler spaces but also offer potential applications in fields such as physics and engineering where Finsler geometry plays a significant role. This work contributes to the ongoing development of Finsler geometry and provides a foundation for future research in this area. The expansion curvature tensor W_ijk^h is an important geometric object in Finsler spaces. It measures the deviation of the geodesic flow from a parallel flow. In this paper, we investigate some identities for the expansion curvature tensor W_ijk^h in Finsler spaces. These identities provide valuable insights into the geometric properties of Finsler spaces and can be used to derive new results in Finsler geometry. We investigate some identities between Weyl Curvature Tensor W_ijk^h and some other curvature tensors.