Closed geodesics on surfaces of genus 0

Wilhelm Klingenberg

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1979)

  • Volume: 6, Issue: 1, page 19-38
  • ISSN: 0391-173X

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Klingenberg, Wilhelm. "Closed geodesics on surfaces of genus 0." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 6.1 (1979): 19-38. <http://eudml.org/doc/83805>.

@article{Klingenberg1979,
author = {Klingenberg, Wilhelm},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {closed geodesics; Lusternik and Schnirelmann theorem; selfintersection number; energy decreasing deformations; surface of genus O},
language = {eng},
number = {1},
pages = {19-38},
publisher = {Scuola normale superiore},
title = {Closed geodesics on surfaces of genus 0},
url = {http://eudml.org/doc/83805},
volume = {6},
year = {1979},
}

TY - JOUR
AU - Klingenberg, Wilhelm
TI - Closed geodesics on surfaces of genus 0
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1979
PB - Scuola normale superiore
VL - 6
IS - 1
SP - 19
EP - 38
LA - eng
KW - closed geodesics; Lusternik and Schnirelmann theorem; selfintersection number; energy decreasing deformations; surface of genus O
UR - http://eudml.org/doc/83805
ER -

References

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  1. [BS] R. Bott - H. Samelson, On the Pontryagin product in spaces of paths, Comm. Math. Helv., 27 (1953), pp. 320-337. Zbl0052.19301MR60233
  2. [GM] D. Gromoll - W. Meyer, Periodic geodesics on compact Riemannian manifolds, J. Diff. Geom., 3 (1969), pp. 493-510. Zbl0203.54401MR264551
  3. [K1] W. Klingenberg, Lectures on Closed Geodesics, Gruadlehren Math. Wiss. Bd. 230Springer, Berlin- Heidelberg-New York, 1968. Zbl0397.58018MR478069
  4. [LS 1] L. Lusternik - L. Schnirelmann, Sur le problème de trois géodésiques fermées sur les surfaces le genre 0, C. R. Acad. Sci. Paris, 189 (1929), pp. 269-271. Zbl55.0316.02JFM55.0316.02
  5. [LS 2] L. Lusternik - L. Schnirelmann, Topological methods in the calculus of variations, Gosudarstv. Izdat. Tehn.-Teor. Lit., Moscow, 1930 (Russian); Méthodes topologiques dans les problèmes variationelles., 1-re partie, Actualités Sci. Industr., no. 188, Paris, 1934. 
  6. [Ly] L. Lyusternik, The topology of function spaces and the calculus of variations in the large, Trudy. Mat. Inst. Steklov, 19 (1947) (Russian); The Topology of the Calculus of Variations in thel arge, Translations of Mathematical Monographs, vol. 16, Amer. Math. Soc., Providence, R.I., 1966. Zbl0154.37003MR25083
  7. [Mo] M. Morse, The calculus of variations in the large, Amer. Math. Soc. Colloq. Publ., vol. 18, Amer. Math. Soc., Providence, R.I., 1934. Zbl0011.02802MR1451874
  8. [Sp] E. Spanier, Algebraic topology, McGraw Hill, New York, 1966. Zbl0145.43303MR210112
  9. [Sv] A.S. Švarc, Homology of the space of closed curves. Trudy Moskov, Mat. Obšv., 9 (1960), pp. 3-44 (Russian). MR133824
  10. [Su] D. Sullivan, Differential forms and the topology of manifolds, Manifolds-Tokyo, 1973, ed. A. HATTORI, Univ. of Tokyo Press, Tokyo, 1975. Zbl0319.58005MR370611

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