INVESTIGATING THE M-PROJECTIVE CURVATURE TENSOR IN GBK-5RFN VIA LIE DERIVATIVES

Abstract

The study of curvature tensors is central to differential geometry, providing insights into the intrinsic and extrinsic properties of manifolds. Among these, the projective curvature tensor has garnered significant attention for its relevance in projective geometry and its applications in physics. Recent developments have focused on generalizing the classical projective curvature tensor to uncover new geometric invariants and broaden the scope of its applications. In this regard, the M-projective curvature tensor has emerged as a notable generalization, offering deeper insights into manifold structures and their geometric behavior. This study examines the properties of the M-projective curvature tensor, highlighting its mathematical significance and potential applications in various space-time models. The analysis employs Lie derivative methods to explore the tensor’s structural characteristics, providing a framework for further investigations in differential geometry and theoretical physics.