Lyusternik–Fet theorem

In mathematics, the Lyusternik–Fet theorem states that on every compact Riemannian manifold there exists a closed geodesic.^[1] It is named after Lazar Lyusternik and Abram Ilyich Fet, who published it in 1951.^[2]

References

1. Anosov, D. V. (2001) [1994], "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)