English

Totally Geodesic Riemannian Foliations on Compact Lie Groups

Differential Geometry 2020-07-15 v4

Abstract

In 86, Ranjan questioned whether a submersion π:GB\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 GG (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

R2 v1 2026-06-22T18:59:23.418Z