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
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.
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
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Metric geometry
Theorems in geometry
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