Geodesic
On the existence of three nonselfintersecting closed geodesics on manifolds homeomorphic to the 2-sphere
Izvestiya. Mathematics, Tome 40 (1993) no. 3, pp. 565-590 
I. A. Taimanov. On the existence of three nonselfintersecting closed geodesics on manifolds homeomorphic to the 2-sphere. Izvestiya. Mathematics, Tome 40 (1993) no. 3, pp. 565-590. http://geodesic.mathdoc.fr/item/IM2_1993_40_3_a4/
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     title = {On~the~existence of three nonselfintersecting closed geodesics on manifolds homeomorphic to the 2-sphere},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The author gives a complete proof of the Lyusternik–Shnirel'man theorem that on each smooth Riemannian manifold homeomorphic to the 2-sphere there exist at least three distinct nonselfintersecting closed geodesics (the proof by Lyusternik and Shnirel'man contains substantial gaps).

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