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- Sub-Riemannian_manifold 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.".
- Sub-Riemannian_manifold wikiPageExternalLink carnot_caratheodory.pdf.
- Sub-Riemannian_manifold wikiPageExternalLink books?id=7Z7IMze7pDwC.
- Sub-Riemannian_manifold wikiPageID "943637".
- Sub-Riemannian_manifold wikiPageLength "5298".
- Sub-Riemannian_manifold wikiPageOutDegree "26".
- Sub-Riemannian_manifold wikiPageRevisionID "594191761".
- Sub-Riemannian_manifold wikiPageWikiLink Carnot_group.
- Sub-Riemannian_manifold wikiPageWikiLink Category:Metric_geometry.
- Sub-Riemannian_manifold wikiPageWikiLink Category:Riemannian_manifolds.
- Sub-Riemannian_manifold wikiPageWikiLink Chow–Rashevskii_theorem.
- Sub-Riemannian_manifold wikiPageWikiLink Classical_mechanics.
- Sub-Riemannian_manifold wikiPageWikiLink Geometric_phase.
- Sub-Riemannian_manifold wikiPageWikiLink Hamiltonian_mechanics.
- Sub-Riemannian_manifold wikiPageWikiLink Hamilton–Jacobi_equation.
- Sub-Riemannian_manifold wikiPageWikiLink Hausdorff_dimension.
- Sub-Riemannian_manifold wikiPageWikiLink Heisenberg_group.
- Sub-Riemannian_manifold wikiPageWikiLink Integer.
- Sub-Riemannian_manifold wikiPageWikiLink Intrinsic_metric.
- Sub-Riemannian_manifold wikiPageWikiLink Lebesgue_covering_dimension.
- Sub-Riemannian_manifold wikiPageWikiLink Lie_group.
- Sub-Riemannian_manifold wikiPageWikiLink Linear_combination.
- Sub-Riemannian_manifold wikiPageWikiLink Manifold.
- Sub-Riemannian_manifold wikiPageWikiLink Mathematics.
- Sub-Riemannian_manifold wikiPageWikiLink Metric_space.
- Sub-Riemannian_manifold wikiPageWikiLink Quadratic_form.
- Sub-Riemannian_manifold wikiPageWikiLink Quantum_mechanics.
- Sub-Riemannian_manifold wikiPageWikiLink Riemannian_manifold.
- Sub-Riemannian_manifold wikiPageWikiLink Sub-Riemannian_manifold.
- Sub-Riemannian_manifold wikiPageWikiLink Subbundle.
- Sub-Riemannian_manifold wikiPageWikiLink Tangent_bundle.
- Sub-Riemannian_manifold wikiPageWikiLinkText "Carnot–Carathéodory metric".
- Sub-Riemannian_manifold wikiPageWikiLinkText "Sub-Riemannian manifold".
- Sub-Riemannian_manifold wikiPageWikiLinkText "sub-Riemannian manifold".
- Sub-Riemannian_manifold wikiPageUsesTemplate Template:Citation.
- Sub-Riemannian_manifold subject Category:Metric_geometry.
- Sub-Riemannian_manifold subject Category:Riemannian_manifolds.
- Sub-Riemannian_manifold hypernym Type.
- Sub-Riemannian_manifold type Diacritic.
- Sub-Riemannian_manifold type Redirect.
- Sub-Riemannian_manifold 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.".
- Sub-Riemannian_manifold label "Sub-Riemannian manifold".
- Sub-Riemannian_manifold sameAs Q7630587.
- Sub-Riemannian_manifold sameAs Variedad_subriemanniana.
- Sub-Riemannian_manifold sameAs m.03s1ff.
- Sub-Riemannian_manifold sameAs Субриманово_многообразие.
- Sub-Riemannian_manifold sameAs Q7630587.
- Sub-Riemannian_manifold wasDerivedFrom Sub-Riemannian_manifold?oldid=594191761.
- Sub-Riemannian_manifold isPrimaryTopicOf Sub-Riemannian_manifold.