Chow–Rashevskii Theorem

(Theorems In Geometry)

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Theorems In Geometry
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What is Chow–Rashevskii theorem?

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 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 .

Technology Types

metric geometrytheorems in geometry

Synonyms

Chow-Rashevskii theoremChow's theorem

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