Pinching constants for hyperbolic manifolds

M. Gromov, W. Thurston

Research output: Contribution to journalArticlepeer-review


We show in this paper that for every n≧4 there exists a closed n-dimensional manifold V which carries a Riemannian metric with negative sectional curvature K but which admits no metric with constant curvature K≡-1. We also estimate the (pinching) constants H for which our manifolds V admit metrics with -1≧K≧-H.

Original languageEnglish (US)
Pages (from-to)1-12
Number of pages12
JournalInventiones Mathematicae
Issue number1
StatePublished - Feb 1987

ASJC Scopus subject areas

  • General Mathematics


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