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
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.