Riemannian homogeneous foliations without holonomy

Abstract

Let M be a compact connected C∞ manifold with a smooth Riemannian foliation ℱ. That is, (M, ℱ) admits a bundle-like metric in the sense of [7]. In [4] it is shown that if all leaves of ℱ are closed without holonomy, then the space of leaves M/ℱ of the foliation is a manifold and the natural projection M → M/ℱ is a locally trivial fibre space. In the present work we show that for certain of the Riemannian homogeneous foliations, holonomy is the only obstruction to the foliation being a fibration.