Remarks on the topology of Lorentzian manifolds (Q2764914)
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scientific article; zbMATH DE number 1691118
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Remarks on the topology of Lorentzian manifolds |
scientific article; zbMATH DE number 1691118 |
Statements
26 June 2002
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Lorentzian manifolds
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1-dimensional distribution
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non-vanishing vector fields
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Remarks on the topology of Lorentzian manifolds (English)
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A smooth manifold having a countable basis in its topology is paracompact. Bu using a partition of unity, it admits a Riemannian metric. This assertion is not true for Lorentzian metrics. The main result of the paper states that a smooth manifold admits a Lorentzian metric if and only if it admits a smooth 1-dimensional distribution. For compact orientable manifolds, this is equivalent to say that there exists a non-vanishing vector field.
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