On 1/4-pinched 4-dimensional Riemannian manifolds of negative curvature (Q1064547)
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scientific article; zbMATH DE number 3919236
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On 1/4-pinched 4-dimensional Riemannian manifolds of negative curvature |
scientific article; zbMATH DE number 3919236 |
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On 1/4-pinched 4-dimensional Riemannian manifolds of negative curvature (English)
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1985
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The following interesting result is proved using integral formulae for characteristic numbers: Let M be a compact oriented 4-dimensional Riemannian manifold with sectional curvature, \(K_ M\), satisfying \(-1\leq K_ M\leq -1/4\). Then the signature \(\tau\) (M), and Euler characteristic, \(\chi\) (M), are related by \(| \tau (M)| \leq (1/3) \chi (M)\). Moreover, equality holds if and only if M is locally isometric to the complex hyperbolic plane.
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integral formulae
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characteristic numbers
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signature
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Euler characteristic
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complex hyperbolic plane
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