Some new examples with almost positive curvature

2008/10/31 by Martin Kerin · 22 citations
Mathematics · #Curvature #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Manifold (fluid mechanics) #Negative curvature #Nonlinear Partial Differential Equations #Quotient #Sectional curvature #math.DG #msc:53C20 #msc:57S25 #msc:57T15

paper · pdf · doi:10.2140/gt.2011.15.217

published in Geometry & Topology 15(1), 217-260 (Mathematical Sciences Publishers) · 43 pages, updated title and abstract, main result and exposition improved

openalex publication_date 2011/02/14 · arxiv created 2012/03/09 · arxiv updated 2014/11/11 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

As a means to better understanding manifolds with positive curvature, there has been much recent interest in the study of nonnegatively curved manifolds which contain points at which all 
\n2
\n–planes have positive curvature. We show that there are generalisations of the well-known Eschenburg spaces and quotients of 
\nS
\n7
\n×
\nS
\n7
\n which admit metrics with this property.

Citations

• Compact Homogeneous Riemannian Manifolds with Strictly Positive Curvature
• An infinite family of distinct 7-manifolds admitting positively curved Riemannian structures
• On the curvature of biquotients

Cited by

• Homogeneous spaces with two equivalent isotropy summands develop positive Ricci curvature under Ricci flow

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• Three new almost positively curved manifolds
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• Topology of non-negatively curved manifolds
• Positively Curved Cohomogeneity One Manifolds and 3-Sasakian Geometry