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Pinching estimates for negatively curved manifolds with nilpotent fundamental groups

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Abstract.

Let M be a complete Riemannian metric of sectional curvature within [−a 2,−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 \(\epsilon > 0,\) the manifold M admits a complete Riemannian metric of sectional curvature within \([ - (k + \epsilon )^2 , - 1].\)

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Authors and Affiliations

  1. School of Mathematics, Georgia Institute of Technology, Atlanta, GA, 30332-0160, USA

    I. Belegradek

  2. Department of Mathematics, University of California, Santa Barbara, CA, 93110, USA

    V. Kapovitch

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  1. I. Belegradek
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  2. V. Kapovitch
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Correspondence to I. Belegradek.

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Received: May 2004 Revision: July 2004 Accepted: July 2004

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Belegradek, I., Kapovitch, V. Pinching estimates for negatively curved manifolds with nilpotent fundamental groups. GAFA, Geom. funct. anal. 15, 929–938 (2005). https://doi.org/10.1007/s00039-005-0534-7

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  • DOI: https://doi.org/10.1007/s00039-005-0534-7

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