A characterization of harmonic foliations by the volume preserving property of the normal geodesic flow
We prove that a Riemannian foliation with the flat normal connection on a Riemannian manifold is harmonic if and only if the geodesic flow on the normal bundle preserves the Riemannian volume form of the canonical metric defined by the adapted connection.
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2002-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171202007822 |
| Summary: | We prove that a Riemannian foliation with the flat normal
connection on a Riemannian manifold is harmonic if and only if
the geodesic flow on the normal bundle preserves the Riemannian
volume form of the canonical metric defined by the adapted connection. |
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| ISSN: | 0161-1712 1687-0425 |