On closed geodesics in the leaf spaces of singular Riemannian foliations

Details On closed geodesics in the leaf spaces of singular Riemannian foliations On closed geodesics in the leaf spaces of singular Riemannian foliations

2009-01-24

arxiv.org/abs/0901.3804v3

Glasgow Mathematical Journal, 53 (2011), pp 555-568

Mathematics

Differential Geometry

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

Scientific paper

10.1017/S0017089511000127

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.

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