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For every sub-Riemannian manifold, there exists a Hamiltonian , called the sub-Riemannian Hamiltonian , constructed out of the metric for the manifold. Conversely, every such quadratic Hamiltonian induces a sub-Riemannian manifold.

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The existence of geodesics of the corresponding Hamilton—Jacobi equations for the sub-Riemannian Hamiltonian is given by the Chow—Rashevskii theorem. From Wikipedia, the free encyclopedia. Categories : Metric geometry Riemannian manifolds.

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The Curve Shortening Problem. Submanifold Theory Beyond an Introduction. Trigonometry A Very Short Introduction.