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arXiv · 0804.0201

Gromov's Pinching Constant

Galina Guzhvina
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Abstract

In early 80's M.Gromov showed that there exists a constant $ε$ such that any compact Riemannian manifold $M^n$ with $|K|_{M^n} \cdot diam^2(M^n) \leq ε$ can be finitely covered by a nilmanifold. The present paper illustrates by an explicit example that the pinching constant $ε$ depends on the dimension $n$ of the manifold, in particular, it decreases with the dimension at least as $\frac{12}{n^2}.$

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Galina Guzhvina. 2008-04-01. Gromov's Pinching Constant. https://arxiv.org/abs/0804.0201

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