Riemannian submersions from simple, compact Lie groups

Abstract

In this paper we construct infinitely many examples of a Riemannian submersion from a simple, compact Lie group $G$ with bi-invariant metric onto a smooth manifold that cannot be a quotient of $G$ by a group action. This partially addresses a question of K. Grove's about Riemannian submersions from Lie groups.

16 pages. Dedicated to J.-H. Eschenburg on the occasion of his 60th birthday