Geometric Analysis and Interaction of Weyl and P₁ Curvature Tensors in Generalized Recurrent Cartan Finsler Spaces

Abstract

The geometric relationship between the P₁-curvature tensor and Weyl's projective curvature tensor in Cartan Finsler spaces is examined in this study. We generate new identities and establish recurrence conditions characterizing their interaction in generalized recurrent Finsler spaces using higher-order Cartan covariant derivatives. Additionally, we examine related tensorial structures, such as the scalar curvature, Ricci tensor, deviation tensor, and torsion tensor, which yield a number of characterization findings. These discoveries add to a better understanding of curvature tensor interactions in non-Riemannian geometric contexts and extend previous findings in Finsler geometry.