On closed geodesics in the leaf spaces of singular Riemannian foliations

Abstract

In this paper we survey on some recent results on Riemannian orbifolds and singular Riemannian foliations and combine them to conclude the existence of closed geodesics in the leaf space of some classes of singular Riemannian foliations (s.r.f.), namely s.r.f. that admit sections or have no horizontal conjugate points. We also investigate the shortening process with respect to Riemannian foliations.

18 pages. A section was expanded and new results were added. The final publication is available at http://journals.cambridge.org/abstract_S0017089511000127

References in corpus (2)

• Proofs of Conjectures about singular riemannian foliations
• Desingularization of singular Riemannian foliation

Cited by in corpus (2)

• On polar foliations and fundamental group
• Geodesics on Riemannian stacks