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.

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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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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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