Unified Geometric Characterization of Hp-Scalar and R³-Like Curvature Structures in Finsler Geometry

Abstract

This paper investigates Finsler spaces with Hp-scalar curvature and explores their intrinsic geometric properties when modeled as -like structures. By analyzing the behavior of curvature tensors under projection and examining relationships between Hp-scalar curvature and p-scalar curvature, we derive new characterizations and a unified curvature identity. We propose a novel theorem combining the projection of curvature tensor, scalar function differentials, and structural identities, providing a new perspective on the geometric configuration of such spaces. These results enrich the understanding of curvature structures in higher-dimensional Finsler spaces and open avenues for application in modern geometric analysis and theoretical physics.