Sub-Riemannian manifold

In mathematics, a sub-Riemannian manifold is a certain type of generalization of a Riemannian manifold. Roughly speaking, to measure distances in a sub-Riemannian manifold,

Related Topics:
Mathematics - Riemannian manifold

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you are allowed to go only along curves tangent to so-called horizontal subspaces.

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Sub-Riemannian manifolds (and so, a fortiori, Riemannian manifolds) carry a natural intrinsic metric called the metric of Carnot-Carathéodory. The Hausdorff dimension of such metric spaces is always an integer and larger than its topological dimension (unless it is actually a Riemannian manifold).

Related Topics:
Intrinsic metric - Hausdorff dimension - Metric space - Integer - Topological dimension

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