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In sub-Riemannian geometry, the Chow–Rashevskii theorem (also known as Chow's theorem) asserts that any two points of a connected sub-Riemannian manifold, endowed with a bracket generating distribution, are connected by a horizontal path in the manifold. It is named after Wei-Liang Chow who proved it in , and , who proved it independently in .

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  • Teorema de Rashevsky–Chow (ca)
  • Chow–Rashevskii theorem (en)
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  • En geometria sub-riemanniana, el teorema de Rashevsky–Chow (també conegut com teorema de Chow) afirma que dos punts qualssevol d'una varietat sub-riemanniana connexa, juntament amb una distribució generada a partir de claudàtors, estan connectats per un camí horitzontal dins de la varietat. Du el nom de Petr Constantinovitx Rashevsky, que el va demostrar l'any i de Wei-Liang Chow que ho va fer també, independentment, l'any . (ca)
  • In sub-Riemannian geometry, the Chow–Rashevskii theorem (also known as Chow's theorem) asserts that any two points of a connected sub-Riemannian manifold, endowed with a bracket generating distribution, are connected by a horizontal path in the manifold. It is named after Wei-Liang Chow who proved it in , and , who proved it independently in . (en)
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  • En geometria sub-riemanniana, el teorema de Rashevsky–Chow (també conegut com teorema de Chow) afirma que dos punts qualssevol d'una varietat sub-riemanniana connexa, juntament amb una distribució generada a partir de claudàtors, estan connectats per un camí horitzontal dins de la varietat. Du el nom de Petr Constantinovitx Rashevsky, que el va demostrar l'any i de Wei-Liang Chow que ho va fer també, independentment, l'any . El teorema es pot expressar en diferents afirmacions equivalents, una de les quals diu que la topologia induïda per la mètrica de Carnot–Carathéodory metric és equivalent a la topologia intrínseca (localment euclidiana) de la varietat. Una afirmació més forta que implica el teorema és el teorema de bola-caixa (ball-box theorem en anglès). Vegi's, per exemple, i . De vegades s'utilitza el terme teorema de Chow per fer referència al següent corol·lari: sigui una varietat connexa i una distribució infinitament diferenciable en , llavors si l'àlgebra de Lie de cobreix tot l'espai tangent de la varietat (és a dir, si ), llavors, per a qualsevol punt , l'òrbita és tota la varietat (és a dir, ). (ca)
  • In sub-Riemannian geometry, the Chow–Rashevskii theorem (also known as Chow's theorem) asserts that any two points of a connected sub-Riemannian manifold, endowed with a bracket generating distribution, are connected by a horizontal path in the manifold. It is named after Wei-Liang Chow who proved it in , and , who proved it independently in . The theorem has a number of equivalent statements, one of which is that the topology induced by the Carnot–Carathéodory metric is equivalent to the intrinsic (locally Euclidean) topology of the manifold. A stronger statement that implies the theorem is the . See, for instance, and . (en)
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