International Journal of Analysis and Applications | 2026
Authors: Sama-Ae A.
DOI: 10.28924/2291-8639-24-2026-9
Journal: International Journal of Analysis and Applications
Year: 2026
Publisher: Etamaths Publishing
Document Type: Article
Open Access: All Open Access; Gold Open Access
Cited by: 0
In this paper, we examine geometric relationships between metric spaces with curvature bounded below and their corresponding model spaces of constant curvature. Let γ be a closed spherical curve in a metric space whose curvature is bounded below by K, lying at a distance (Formula presented) from a point. Let γ′ denote the circle of radius r centered at the corresponding point in the model space of constant curvature K. Under suitable geometric equivalence conditions—namely, the preservation of pairwise distances between corresponding points of γ and γ′, the isometry of convex hulls of corresponding geodesic triangles, and the equality of arc lengths or total curvature—we show that the geodesic surface enclosed by γ is isometric to the region bounded by γ′. This result offers a foundational geometric characterization of metric spaces with curvature bounded below through their model counterparts and provides a framework for further study of total curvature, convexity, and isometric embeddings in such spaces. © 2026 the author(s).
isometry; metric spaces with lower curvature bounds; spherical curve; total curvature