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A characterization of harmonic foliations by the volume preserving property of the normal geodesic flow

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  • Hobum Kim

Abstract

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.

Suggested Citation

  • Hobum Kim, 2002. "A characterization of harmonic foliations by the volume preserving property of the normal geodesic flow," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 29, pages 1-5, January.
    • Handle: RePEc:hin:jijmms:651316
    DOI: 10.1155/S0161171202007822
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