## 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
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## 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 â€śshortestâ€ť Lusternik-Schnirelmann closed geodesic $c$ is isolated and â€śnonrotatingâ€ť.## 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