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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 1939, and Petr Konstanovich Rashevskii, who proved it independently in
1938 Events January * January 1 – state-owned enterprise, State-owned railway networks are created by merger, in France (SNCF) and the Netherlands (Nederlandse Spoorwegen – NS). * January 20 – King Farouk of Egypt marries Saf ...
. 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 ball–box theorem. See, for instance, and .


See also

* Orbit (control theory)


References

* * * * Metric geometry Theorems in geometry {{differential-geometry-stub