Pinching estimates for negatively curved manifolds with nilpotent fundamental groups

2004/05/30 by Igor Belegradek, Vitali Kapovitch, Belegradek, Igor +1
Mathematics · #53C20 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53C20

paper · pdf · doi:10.48550/arxiv.math/0405579

formula corrected, see page 7

arxiv created 2010/08/28 · arxiv updated 2010/08/31

Abstract

Let M be a complete Riemannian metric of sectional curvature within [-a²,-1] whose fundamental group contains a k-step nilpotent subgroup of finite index. We prove that a≥ k answering a question of M. Gromov. Furthermore, we show that for any ε>0, the manifold M admits a complete Riemannian metric of sectional curvature within [-(k+ε)²,-1].

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