mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

, the Lyusternik–Fet theorem states that on every compact

Riemannian manifold In differential geometry, a Riemannian manifold or Riemannian space , so called after the German mathematician Bernhard Riemann, is a real manifold, real, smooth manifold ''M'' equipped with a positive-definite Inner product space, inner product ...

there exists a

closed geodesic In differential geometry and dynamical systems, a closed geodesic on a Riemannian manifold is a geodesic that returns to its starting point with the same tangent direction. It may be formalized as the projection of a closed orbit of the geodesic, ge ...

. It is named after

Lazar Lyusternik Lazar Aronovich Lyusternik (also Lusternik, Lusternick, Ljusternik; ; 31 December 1899, in Zduńska Wola, Congress Poland, Russian Empire – 23 July 1981, in Moscow, Soviet Union) was a Soviet mathematician. He is famous for his work in topolog ...

and

Abram Ilyich Fet Abram Fet (russian: Абрам Ильич Фет) (5 December 1924 — 30 July 2009) was a Russian mathematician, Soviet dissident, philosopher, Samizdat translator and writer. He used various pseudonyms for Samizdat, like N. A. Klenov, A.B. N ...

References

* https://www.encyclopediaofmath.org/index.php/Closed_geodesic * L.A. Lyusternik, A.I. Fet, "Variational problems on closed manifolds" Dokl. Akad. Nauk. SSSR, 81 (1951) pp. 17–18 (In Russian) Differential geometry Geodesic (mathematics) {{DEFAULTSORT:Lyusternik-Fet theorem