On the Generalized Projective Riemann Curvature in Finsler Geometry

Abstract: This paper explores the generalized projective Riemann curvature in Finsler geometry, focusing on the properties of projectively equivalent Finsler metrics and the invariance of their curvature structures under projective transformations. We extend the existing frameworks of projective Riemann and Ricci curvatures by introducing new characterizations of quadratic curvature properties, highlighting their geometric significance in the broader context of Finsler manifolds. Our results provide novel insights into curvature behavior under generalized projective sprays and contribute to a deeper understanding of intrinsic geometric invariants within projective classes of Finsler spaces.