Totally Geodesic Riemannian Foliations on Compact Lie Groups
Differential Geometry
2020-07-15 v4
Abstract
In 86, Ranjan questioned whether a submersion 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 (assuming suitable hypothesis).
Cite
@article{arxiv.1703.09577,
title = {Totally Geodesic Riemannian Foliations on Compact Lie Groups},
author = {Llohann D. Sperança},
journal= {arXiv preprint arXiv:1703.09577},
year = {2020}
}
Comments
26 pages. Renewed version with a simplified proof and a new local statement