International Journal of Mathematics and Mathematical Sciences
Volume 29 (2002), Issue 10, Pages 573-577
doi:10.1155/S0161171202007822

A characterization of harmonic foliations by the volumepreserving property of the normal geodesic flow

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.