Riemannian foliations on contractible manifolds

Abstract

We prove that Riemannian foliations on complete contractible manifolds have a closed leaf, and that all leaves are closed if one closed leaf has a finitely generated fundamental group. Under additional topological or geometric assumptions we prove that the foliation is also simple.

14 pages

References in corpus (1)

• Geometrization of Three-Dimensional Orbifolds via Ricci Flow

Cited by in corpus (2)

• A-Foliations of codimension two on compact simply-connected manifolds
• Rigidity theorems for submetries in positive curvature