Pinching estimates for negatively curved manifolds with nilpotent fundamental groups

Details Pinching estimates for negatively curved manifolds with nilpotent fundamental groups Pinching estimates for negatively curved manifolds with nilpotent fundamental groups

2004-05-30

arxiv.org/abs/math/0405579v3

Mathematics

Differential Geometry

formula corrected, see page 7

Scientific paper

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

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