Abstract

This paper investigates the relationship between Cartan’s second curvature tensor and Weyl’s projective curvature tensor in the context of Riemannian spaces. The study focuses on deriving a formula that connects these two curvature tensors and exploring the implications of their interactions. Key results of this work include the establishment of a set of equations that describe the covariance and transvectivity of these tensors under various conditions, leading to the formulation of several theorems. The findings provide new insights into generalized birecurrent Finsler spaces and their geometric properties, contributing to the understanding of curvature tensors in higher-dimensional spaces.