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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the lengths of closed geodesics on a two-sphere
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by Nancy Hingston
Proc. Amer. Math. Soc. 125 (1997), 3099-3106
DOI: https://doi.org/10.1090/S0002-9939-97-04235-4

Abstract:

Let $c$ be an isolated closed geodesic of length $L$ on a compact Riemannian manifold $M$ which is homologically visible in the dimension of its index, and for which the index of the iterates has the maximal possible growth rate. We show that $M$ has a sequence $\{c_n\}$, $n\in \mathbb {Z}^+$, of prime closed geodesics of length $m_nL-\varepsilon _n$ where $m_n\in \mathbb {Z}$ and $\varepsilon _n\downarrow 0$. The hypotheses hold in particular when $M$ is a two-sphere and the “shortest” Lusternik-Schnirelmann closed geodesic $c$ is isolated and “nonrotating”.
References
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Bibliographic Information
  • Nancy Hingston
  • Affiliation: Department of Mathematics, The College of New Jersey, Trenton, New Jersey 08650
  • Email: hingston@tcnj.edu
  • Received by editor(s): April 2, 1996
  • Communicated by: Christopher Croke
  • © Copyright 1997 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 125 (1997), 3099-3106
  • MSC (1991): Primary 58E10; Secondary 53C22
  • DOI: https://doi.org/10.1090/S0002-9939-97-04235-4
  • MathSciNet review: 1443831