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Riemannian rigidity of the parallel postulate in total curvature

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Publication:2290800
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DOI10.1007/s00208-019-01883-8zbMath1434.53044arXiv1611.07761OpenAlexW2968099951WikidataQ115388915 ScholiaQ115388915MaRDI QIDQ2290800

Yanyan Li

Publication date: 29 January 2020

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.07761


zbMATH Keywords

Euclidean geometryparallel postulatetotal curvature


Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20) Rigidity results (53C24) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23)


Related Items

Bounded distance geodesic foliations in Riemannian planes



Cites Work

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  • Area growth and rigidity of surfaces without conjugate points
  • Rigidity of surfaces with no conjugate points
  • Planes without conjugate points
  • The integral of the scalar curvature of complete manifolds without conjugate points
  • Riemannian tori without conjugate points are flat
  • A synthetic characterization of the hemisphere
  • Closed Surfaces Without Conjugate Points
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