Some Principles for Deforming Nonnegative Curvature

2009/08/20 by Peter Petersen, Petersen, Peter, Frederick Wilhelm +1
Mathematics · Physics and Astronomy · #53C20 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG #msc:53C20

paper · pdf · doi:10.48550/arxiv.0908.3026

42 pages. This is part of a revision of the manuscript that describes how to deform the Gromoll-Meyer metric to positive curvature, see arXiv:0805.0812. This paper has been significantly expanded and corrected in a few places

openalex publication_date 2009/08/20 · arxiv created 2010/02/23 · arxiv updated 2010/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe a few abstract principles that are used in the deformation of the Gromoll-Meyer metric to positive curvature.

Citations

• A positively curved manifold homeomorphic to T₁S⁴
• Flats in Riemannian Submersions from Lie Groups
• Lifting Group Actions and Nonnegative Curvature
• An exotic sphere with positive sectional curvature

Related

• Conditions for Nonnegative Curvature on Vector Bundles and Sphere Bundles
• Developments around positive sectional curvature
• An exotic sphere with positive sectional curvature
• Nonnegatively and Positively curved manifolds
• Analysis, Geometry and Topology of Positive Scalar Curvature Metrics