Totally Geodesic Riemannian Foliations on Compact Lie Groups

Abstract

In 86, Ranjan questioned whether a submersion $\pi :G\to B$ from a compact simple Lie group with bi-invariant metric is a coset foliation or not, provided the submersion is Riemannian with totally geodesic fibers. Here we answer this question affirmatively, even when the submersion is defined only in an open subset of $G$ (assuming suitable hypothesis).

26 pages. Renewed version with a simplified proof and a new local statement

References in corpus (3)

• Riemannian foliations of spheres
• Riemannian submersions from simple, compact Lie groups
• Holonomy Groups in Riemannian Geometry

Cited by in corpus (1)

• An intrinsic curvature condition for submersions over Riemannian manifolds