Harmonic foliations on a complete Riemannian manifold (Q1433473)
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scientific article; zbMATH DE number 2076000
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Harmonic foliations on a complete Riemannian manifold |
scientific article; zbMATH DE number 2076000 |
Statements
Harmonic foliations on a complete Riemannian manifold (English)
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18 June 2004
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Let \(M\) be a manifold with complete bundle-like metric \(g_M\). Let \(\mathcal F\) be a Riemannian foliation of \(M\) with finite energy. Assume that the Ricci curvature \(\rho^M\) on \(M\) is non-negative and the transversal scalar curvature is non-positive. Then if \(\mathcal F\) is harmonic then \(\mathcal F\) is totally geodesic.
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Riemannian manifold
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bundle-like metric
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Riemannian foliation
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harmonic foliation
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Ricci curvature
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scalar curvature
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