标题： 格罗莫夫的夹紧常数 显示英文标题

标题： Gromov's Pinching Constant

摘要： 在80年代初，M.Gromov证明了存在一个常数$\epsilon$，使得任何紧致黎曼流形$M^n$如果满足$|K|_{M^n} \cdot diam^2(M^n) \leq \epsilon$，则可以被一个幂零流形有限覆盖。 本文通过一个具体的例子说明，夹挤常数$\epsilon$依赖于流形的维数$n$，特别是，它随着维数的增加至少按$\frac{12}{n^2}.$的速度减小。 显示英文摘要

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