Duke Mathematical Journal

On the number of closed geodesics on a compact Riemannian manifold

Werner Ballmann and Wolfgang Ziller

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Article information

Source
Duke Math. J., Volume 49, Number 3 (1982), 629-632.

Dates
First available in Project Euclid: 20 February 2004

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1077315381

Digital Object Identifier
doi:10.1215/S0012-7094-82-04932-8

Mathematical Reviews number (MathSciNet)
MR672499

Zentralblatt MATH identifier
0495.53042

Subjects
Primary: 53C22: Geodesics [See also 58E10]
Secondary: 58E10: Applications to the theory of geodesics (problems in one independent variable)

Citation

Ballmann, Werner; Ziller, Wolfgang. On the number of closed geodesics on a compact Riemannian manifold. Duke Math. J. 49 (1982), no. 3, 629--632. doi:10.1215/S0012-7094-82-04932-8. https://projecteuclid.org/euclid.dmj/1077315381


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References

  • [1] R. Abraham, Bumpy metrics, Global Analysis (Proc. Sympos. Pure Math., Vol. XIV, Berkeley, Calif., 1968), Amer. Math. Soc., Providence, R.I., 1970, pp. 1–3.
  • [2] W. Ballmann, G. Thorbergsson, and W. Ziller, Closed geodesics on positively curved manifolds, Ann. of Math. (2) 116 (1982), no. 2, 213–247.
  • [3] R. Bott, On the iteration of closed geodesics and the Sturm intersection theory, Comm. Pure Appl. Math. 9 (1956), 171–206.
  • [4] D. Gromoll and W. Meyer, Periodic geodesics on compact riemannian manifolds, J. Differential Geometry 3 (1969), 493–510.
  • [5] M. Gromov, Homotopical effects of dilatation, J. Differential Geom. 13 (1978), no. 3, 303–310.
  • [6] W. Klingenberg, Lectures on closed geodesics, Springer-Verlag, Berlin, 1978.