International Journal of Mathematics and Mathematical Sciences
Volume 29 (2002), Issue 10, Pages 573-577

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

Hobum Kim

Department of Mathematics, Yonsei University, Seoul 120-749, Korea

Received 22 July 2001

Copyright © 2002 Hobum Kim. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.