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Klingenberg, Wilhelm

Closed geodesics on surfaces of genus O. (English) Zbl 0426.58008

Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 6, 19-38 (1979).
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scan of Zbl 0426.58008

Cited in 2 Documents

MSC:

58E10 Variational problems in applications to the theory of geodesics (problems in one independent variable)
53C22 Geodesics in global differential geometry
53C20 Global Riemannian geometry, including pinching

Keywords:

closed geodesics; Lusternik and Schnirelmann theorem; selfintersection number; energy decreasing deformations; surface of genus O

Citations:

Zbl 0397.58018
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Full Text: Numdam EuDML

References:

[1] R. Bott - H. Samelson , On the Pontryagin product in spaces of paths , Comm. Math. Helv. , 27 ( 1953 ), pp. 320 - 337 . MR 60233 | Zbl 0052.19301 · Zbl 0052.19301 · doi:10.1007/BF02564566
[2] D. Gromoll - W. Meyer , Periodic geodesics on compact Riemannian manifolds , J. Diff. Geom. , 3 ( 1969 ), pp. 493 - 510 . MR 264551 | Zbl 0203.54401 · Zbl 0203.54401
[3] W. Klingenberg , Lectures on Closed Geodesics, Gruadlehren Math. Wiss. Bd. 230 Springer , Berlin - Heidelberg - New York , 1968 . MR 478069 | Zbl 0397.58018 · Zbl 0397.58018
[4] 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 . JFM 55.0316.02 · JFM 55.0316.02
[5] 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] 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 . MR 25083 | Zbl 0154.37003 · Zbl 0154.37003
[7] M. Morse , The calculus of variations in the large, Amer. Math. Soc. Colloq. Publ. , vol. 18 , Amer. Math. Soc ., Providence, R.I. , 1934 . MR 1451874 | Zbl 0011.02802 · Zbl 0011.02802
[8] E. Spanier , Algebraic topology , McGraw Hill , New York , 1966 . MR 210112 | Zbl 0145.43303 · Zbl 0145.43303
[9] A.S. Švarc , Homology of the space of closed curves. Trudy Moskov, Mat. Obšv. , 9 ( 1960 ), pp. 3 - 44 (Russian). MR 133824
[10] D. Sullivan , Differential forms and the topology of manifolds, Manifolds-Tokyo, 1973 , ed. A. HATTORI, Univ. of Tokyo Press , Tokyo , 1975 . MR 370611 | Zbl 0319.58005 · Zbl 0319.58005
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