Geometry of Riemannian submersions and differential invariants.

This article proves that on a manifold with zero sectional curvature, if the submersion is Riemannian, then the foliation is a completely geodesic Riemannian foliation with isometric fibers. In addition, it is shown that if each component of the critical level surface is either a point or a regular surface, and they are isolated from each other, then the level surfaces of the function are conformally equivalent. [ABSTRACT FROM AUTHOR]