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ON CLOSED GEODESICS IN THE LEAF SPACE OF SINGULAR RIEMANNIAN FOLIATIONS

Published online by Cambridge University Press:  10 March 2011

MARCOS M. ALEXANDRINO  and
MIGUEL ANGEL JAVALOYES
MARCOS M. ALEXANDRINO
Affiliation:
Instituto de Matemática e Estatística Universidade de São Paulo, Rua do Matão 1010,05508 090 São Paulo, Brazil e-mail: marcosmalex@yahoo.de, malex@ime.usp.br
MIGUEL ANGEL JAVALOYES
Affiliation:
Departamento de Geometría y Topología. Facultad de Ciencias, Universidad de Granada. Campus Fuentenueva s/n, 18071 Granada, Spain e-mail: majava@ugr.es, ma.javaloyes@gmail.com
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Abstract

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In this paper we prove the existence of closed geodesics in the leaf space of some classes of singular Riemannian foliations (s.r.f.), namely s.r.fs. that admit sections or have no horizontal conjugate points. We also investigate the shortening process with respect to Riemannian foliations.

Keywords

Primary 53C12Secondary 57R30
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 53 , Issue 3 , September 2011 , pp. 555 - 568
Copyright
Copyright © Glasgow Mathematical Journal Trust 2011

References

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