A fiber bundle theorem (Q1201424)
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scientific article; zbMATH DE number 97885
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A fiber bundle theorem |
scientific article; zbMATH DE number 97885 |
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A fiber bundle theorem (English)
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17 January 1993
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The author proves that a surjective submersion \(\pi: M\to B\) from a pseudo-Riemannian manifold \(M\) is a fibre bundle, if its fibres are connected totally geodesic and geodesically complete submanifolds of \(M\). This theorem is ``dual'' to R. Hermann's result (1960) about Riemannian submersions and based on the observation that if the surjective submersion \(\pi: M\to B\) admits an Ehresmann connection (distribution on \(M\) which is complementary to the fibers with whole lifts for every curve in \(B\)), then it is a fibre bundle.
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totally geodesic submanifold
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submersion
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Ehresmann connection
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