On the curvature of biquotients

2008/09/30 by Martin Kerin · 20 citations
Mathematics · #Advanced Operator Algebra Research #Curvature #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Manifold (fluid mechanics) #Open set #Point (geometry) #Quotient #Set (abstract data type) #Torus #math.DG #msc:53C20 #msc:53C30 #msc:57R18

paper · pdf · doi:10.1007/s00208-011-0634-7

published in Mathematische Annalen 352(1), 155-178 (Springer Nature) · V3 An error has been discovered in Section 3. This section has been removed and the Introduction modified accordingly; V4 published version

openalex publication_date 2011/01/21 · arxiv created 2012/03/09 · arxiv updated 2012/03/12 · 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 non-negatively curved manifolds which contain either a point or an open dense set of points at which all 2-planes have positive curvature. We study infinite families of biquotients defined by Eschenburg and Bazaikin from this viewpoint, together with torus quotients of S³ \x S³.

Citations

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

Cited by

• Some new examples with almost positive curvature
• A knot characterization and 1–connected nonnegatively curved 4–manifolds with circle symmetry