Examples of Manifolds with Non-negative Sectional Curvature

2006/01/01 by Wolfgang Ziller · 1 citation
Mathematics · Physics and Astronomy · Engineering · #Geometric Analysis and Curvature Flows #Advanced Differential Geometry Research #Advanced Numerical Analysis Techniques #Sectional curvature #Curvature #Negative curvature #Mathematics #Geology #Pure mathematics #Geometry #Scalar curvature

paper · pdf · doi:10.4310/sdg.2006.v11.n1.a4

openalex publication_date 2006/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/04/21

Abstract

Manifolds with non-negative sectional curvature have been of interest since the beginning of global Riemannian geometry, as illustrated by the theorems of Bonnet-Myers, Synge, and the sphere theorem. Some of the oldest conjectures in global Riemannian geometry, as for example the Hopf conjecture on S 2 S 2 , also fit into this subject.

Citations

• Three-manifolds with positive Ricci curvature
• Compact Homogeneous Riemannian Manifolds with Strictly Positive Curvature
• Contributions of rational homotopy theory to global problems in geometry
• Lifting Group Actions and Nonnegative Curvature

Cited by

• Sectional curvature [wikipedia]