A Study of the M-Projective Curvature Tensor in Generalized Recurrent and Birecurrent Finsler Spaces

Abstract

This paper aims to examine the properties of the M-projective curvature tensor in the context of generalized Finsler spaces, specifically within the framework of a -space. The study begins with the derivation of the M-projective curvature tensor, which is expressed as the sum of the standard M-projective curvature tensor and additional terms involving the Ricci tensor and scalar curvature. Through covariant differentiation, the behavior of this tensor under certain conditions is analyzed, leading to a set of conditions necessary for the space to exhibit generalized recurrent Finsler properties. The paper includes multiple theorems that explore these relationships, proving that the M-projective curvature tensor satisfies the conditions for generalized recurrent Finsler spaces. Additionally, the work introduces the concept of generalized birecurrent Finsler spaces and presents several characterization theorems. Finally, the results are corroborated with computational formulations that demonstrate the conditions under which the tensor relationships hold true.