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- Q7630587 subject Q7413945.
- Q7630587 subject Q8662693.
- Q7630587 abstract "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, you are allowed to go only along curves tangent to so-called horizontal subspaces.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).Sub-Riemannian manifolds often occur in the study of constrained systems in classical mechanics, such as the motion of vehicles on a surface, the motion of robot arms, and the orbital dynamics of satellites. Geometric quantities such as the Berry phase may be understood in the language of sub-Riemannian geometry. The Heisenberg group, important to quantum mechanics, carries a natural sub-Riemannian structure.".
- Q7630587 wikiPageExternalLink carnot_caratheodory.pdf.
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- Q7630587 wikiPageWikiLink Q632814.
- Q7630587 wikiPageWikiLink Q736753.
- Q7630587 wikiPageWikiLink Q7413945.
- Q7630587 wikiPageWikiLink Q746550.
- Q7630587 wikiPageWikiLink Q7630587.
- Q7630587 wikiPageWikiLink Q7630879.
- Q7630587 wikiPageWikiLink Q8662693.
- Q7630587 wikiPageWikiLink Q944.
- Q7630587 comment "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, you are allowed to go only along curves tangent to so-called horizontal subspaces.Sub-Riemannian manifolds (and so, a fortiori, Riemannian manifolds) carry a natural intrinsic metric called the metric of Carnot–Carathéodory.".
- Q7630587 label "Sub-Riemannian manifold".