| dbo: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) |
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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) |
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Teorema tiga geodesik (in) Theorem of the three geodesics (en) Теорема про три геодезичні (uk) |
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