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Upper bounds on the length of a shortest closed geodesic and quantitative Hurewicz theorem

Upper bounds on the length of a shortest closed geodesic and quantitative Hurewicz theorem In this paper we present two upper bounds on the length of a shortest closed geodesic on compact Riemannian manifolds. The first upper bound depends on an upper bound on sectional curvature and an upper bound on the volume of the manifold. The second upper bound will be given in terms of a lower bound on sectional curvature, an upper bound on the diameter and a lower bound on the volume. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of the European Mathematical Society Springer Journals

Upper bounds on the length of a shortest closed geodesic and quantitative Hurewicz theorem

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Publisher
Springer Journals
Copyright
Copyright © 2003 by Springer-Verlag
Subject
Mathematics
ISSN
1435-9855
eISSN
1435-9863
DOI
10.1007/s10097-003-0051-7
Publisher site
See Article on Publisher Site

Abstract

In this paper we present two upper bounds on the length of a shortest closed geodesic on compact Riemannian manifolds. The first upper bound depends on an upper bound on sectional curvature and an upper bound on the volume of the manifold. The second upper bound will be given in terms of a lower bound on sectional curvature, an upper bound on the diameter and a lower bound on the volume.

Journal

Journal of the European Mathematical Society – Springer Journals

Published: Jun 6, 2003

References