Pinching constants for hyperbolic manifolds
This paper exhibits very interesting examples of n-manifolds M, \(n\geq 4\), with negative sectional curvature, \(K_ M\). On the one hand, for every \(k<-1\) there is a closed negatively curved manifold M, which carries no metric satisfying \(k\leq K_ M\leq -1\). On the other hand for any \(k<-1\) there is a closed manifold M with \(k\leq K_ m\leq -1\) which does not carry a metric with constant negative curvature. This latter statement is in sharp contrast to the situation for positively curved manifolds [cf. the reviewer, \textit{H. Karcher} and \textit{E. A. Ruh}, Invent. Math. 23, 31- 48 (1974; Zbl 0271.53044); Math. Ann. 211, 7-21 (1974; Zbl 0273.53051)].
scientific article; zbMATH DE number 4054503