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Pinching estimates for negatively curved manifolds with nilpotent fundamental groups

Igor Belegradek·Vitali Kapovitch
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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 $a\ge k$ 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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Igor Belegradek, Vitali Kapovitch. 2010-08-28. Pinching estimates for negatively curved manifolds with nilpotent fundamental groups. https://arxiv.org/abs/math/0405579

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