Classification of negatively pinched manifolds with amenable fundamental\n groups

2004/02/16 by Igor Belegradek, Vitali Kapovitch, Belegradek, Igor +1
Engineering · Mathematics · #53C20 #Combinatorics #Diffeomorphism #Differential Geometry (math.DG) #Engineering #FOS: Mathematics #Fundamental group #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry #Geometry and complex manifolds #Line (geometry) #Manifold (fluid mechanics) #Mathematical analysis #Mathematics #Pure mathematics #Topology (electrical circuits) #math.DG #msc:53C20

paper · pdf · doi:10.48550/arxiv.math/0402268

formula corrected, see page 24

openalex publication_date 2004/02/16 · arxiv created 2010/08/28 · arxiv updated 2010/08/31 · openalex created_date 2025/10/24 · openalex updated_date 2026/08/06

Abstract

We give a diffeomorphism classification of pinched negatively curved\nmanifolds with amenable fundamental groups, namely, they are precisely the\nM "obius band, and the products of a line with the total spaces of flat vector\nbundles over closed infranilmanifolds.\n

Citations

• Comparison Theorems in Riemannian Geometry
• Manifolds of negative curvature
• Metrics of positive Ricci curvature on bundles

Related

• Kähler manifolds and fundamental groups of negatively δ-pinched manifolds
• A remark on the fundamental group of a compact negatively curved manifold
• Classification of manifolds with weakly 1/4-pinched curvatures
• Pinching estimates for negatively curved manifolds with nilpotent fundamental groups
• Counting open negatively curved manifolds up to tangential homotopy equivalence