About: Theorem of the three geodesics

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In differential geometry the theorem of the three geodesics, also known as Lyusternik–Schnirelmann theorem, states that every Riemannian manifold with the topology of a sphere has at least three simple closed geodesics (i.e. three embedded geodesic circles). The result can also be extended to quasigeodesics on a convex polyhedron, and to closed geodesics of reversible Finsler 2-spheres. The theorem is sharp: although every Riemannian 2-sphere contains infinitely many distinct closed geodesics, only three of them are guaranteed to have no self-intersections. For example, by a result of Morse if the lengths of three principal axes of an ellipsoid are distinct, but sufficiently close to each other, then the ellipsoid has only three simple closed geodesics.

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rdfs:label	Teorema tiga geodesik (in) Theorem of the three geodesics (en) Теорема про три геодезичні (uk)
rdfs:comment	Dalam geometri diferensial, teorema tiga geodetik atau teorema Lyusternik–Schnirelmann menyatakan bahwa setiap manifold Riemann dengan topologi bola setidaknya memiliki tiga yang membentuk tanpa perpotongan-diri. Hasilnya juga dapat diperluas ke kuasigeodesik pada polihedron cembung. (in) In differential geometry the theorem of the three geodesics, also known as Lyusternik–Schnirelmann theorem, states that every Riemannian manifold with the topology of a sphere has at least three simple closed geodesics (i.e. three embedded geodesic circles). The result can also be extended to quasigeodesics on a convex polyhedron, and to closed geodesics of reversible Finsler 2-spheres. The theorem is sharp: although every Riemannian 2-sphere contains infinitely many distinct closed geodesics, only three of them are guaranteed to have no self-intersections. For example, by a result of Morse if the lengths of three principal axes of an ellipsoid are distinct, but sufficiently close to each other, then the ellipsoid has only three simple closed geodesics. (en) У диференціальній геометрії теорема про три геодезичні стверджує, що кожен ріманів многовид з топологією сфери має три замкнені геодезичні, які є простими замкненими кривими без самоперетинів. Теорема також буде вірною для випадку квазігеодезичних ліній на поверхні опуклого многогранника. (uk)
foaf:depiction
dcterms:subject	Geodesic (mathematics) Theorems in differential geometry
Wikipage page ID	48445265 (xsd:integer)
Wikipage revision ID	1121530193 (xsd:integer)
Link from a Wikipage to another Wikipage	Regular tetrahedron Riemann surface Maryam Mirzakhani Geodesic (mathematics) Ellipsoid Geodesic Geodesics on an ellipsoid Great circle Lev Schnirelmann Line (geometry) Closed geodesic Disphenoid Curve shortening flow Open problem Almost all Angular defect Riemannian manifold Henri Poincaré Theorems in differential geometry Hyperbolic geometry Lazar Lyusternik Homeomorphism Differential geometry Marston Morse Sphere Convex polyhedron Polynomial time Euclidean plane Selberg zeta function Finsler Finsler metric
sameAs	Theorem of the three geodesics Theorem of the three geodesics Theorem of the three geodesics Theorem of the three geodesics Theorem of the three geodesics Theorem of the three geodesics
dbp:wikiPageUsesTemplate	dbt:Pi dbt:Reflist dbt:Short_description dbt:Unsolved
thumbnail	wiki-commons:Special:FilePath/Ellipsoid_tri-axial_abc.svg?width=300
has abstract	Dalam geometri diferensial, teorema tiga geodetik atau teorema Lyusternik–Schnirelmann menyatakan bahwa setiap manifold Riemann dengan topologi bola setidaknya memiliki tiga yang membentuk tanpa perpotongan-diri. Hasilnya juga dapat diperluas ke kuasigeodesik pada polihedron cembung. (in) In differential geometry the theorem of the three geodesics, also known as Lyusternik–Schnirelmann theorem, states that every Riemannian manifold with the topology of a sphere has at least three simple closed geodesics (i.e. three embedded geodesic circles). The result can also be extended to quasigeodesics on a convex polyhedron, and to closed geodesics of reversible Finsler 2-spheres. The theorem is sharp: although every Riemannian 2-sphere contains infinitely many distinct closed geodesics, only three of them are guaranteed to have no self-intersections. For example, by a result of Morse if the lengths of three principal axes of an ellipsoid are distinct, but sufficiently close to each other, then the ellipsoid has only three simple closed geodesics. (en) У диференціальній геометрії теорема про три геодезичні стверджує, що кожен ріманів многовид з топологією сфери має три замкнені геодезичні, які є простими замкненими кривими без самоперетинів. Теорема також буде вірною для випадку квазігеодезичних ліній на поверхні опуклого многогранника. (uk)
prov:wasDerivedFrom	wikipedia-en:Theorem_of_the_three_geodesics?oldid=1121530193&ns=0
page length (characters) of wiki page	11483 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Theorem_of_the_three_geodesics
is Link from a Wikipage to another Wikipage of	List of incomplete proofs Maryam Mirzakhani Alexandrov's uniqueness theorem Theorem of the three closed geodesics Lev Schnirelmann Closed geodesic Curve-shortening flow Lazar Lyusternik List of unsolved problems in computer science NP-intermediate Lusternik-Schnirelmann theorem of the three closed geodesics Lusternik-Schnirelmann theorem of the three geodesics Lusternik–Schnirelmann theorem of the three closed geodesics Lusternik–Schnirelmann theorem of the three geodesics
is Wikipage redirect of	Theorem of the three closed geodesics Lusternik-Schnirelmann theorem of the three closed geodesics Lusternik-Schnirelmann theorem of the three geodesics Lusternik–Schnirelmann theorem of the three closed geodesics Lusternik–Schnirelmann theorem of the three geodesics
is foaf:primaryTopic of	wikipedia-en:Theorem_of_the_three_geodesics

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