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In mathematics, the Lyusternik–Fet theorem states that on every compact Riemannian manifold there exists a closed geodesic. It is named after Lazar Lyusternik and Abram Ilyich Fet, who published it in 1951.

References

1. Anosov, D. V. (2001) , "Closed geodesic", Encyclopedia of Mathematics, EMS Press
2. L.A. Lyusternik, A.I. Fet, "Variational problems on closed manifolds" Dokl. Akad. Nauk. SSSR, 81 (1951) pp. 17–18 (In Russian)

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