Pinching constants for hyperbolic manifolds

M. Gromov; W. Thurston

doi:10.1007/BF01404671

Pinching constants for hyperbolic manifolds

M. Gromov, W. Thurston

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English (US)
Pages (from-to)	1-12
Number of pages	12
Journal	Inventiones Mathematicae
Volume	89
Issue number	1
DOIs	https://doi.org/10.1007/BF01404671
State	Published - Feb 1987

ASJC Scopus subject areas

General Mathematics

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title = "Pinching constants for hyperbolic manifolds",

abstract = "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.",

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AB - 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.

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Pinching constants for hyperbolic manifolds

Abstract

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