Riemannian Rigidity of the Parallel Postulate in Total Curvature

2016/11/23 by Jian Ge, Luis Guijarro, Ge, Jian +3
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematics and Applications #math.DG

paper · pdf · doi:10.48550/arxiv.1611.07761

arxiv created 2016/11/23 · openalex publication_date 2016/11/23 · arxiv updated 2016/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the Euclidean plane is the only Riemannian plane with total curvature and free of conjugate points that satisfies Playfair's version of the parallel postulate.

Related

• Is Parallel Postulate Necessary?
• Remarks on a scalar curvature rigidity theorem of Brendle and Marques
• Deformation principle and problem of parallelism in geometry and physics
• A dual rigidity of the sphere and the hyperbolic plane
• On the equivalence of Playfair's axiom to the parallel postulate