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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 books?id=7Z7IMze7pDwC.
- Sub-Riemannian_manifold wikiPageExternalLink carnot_caratheodory.pdf.
- Sub-Riemannian_manifold wikiPageID "943637".
- Sub-Riemannian_manifold wikiPageRevisionID "594191761".
- Sub-Riemannian_manifold hasPhotoCollection Sub-Riemannian_manifold.
- Sub-Riemannian_manifold subject Category:Metric_geometry.
- Sub-Riemannian_manifold subject Category:Riemannian_manifolds.
- Sub-Riemannian_manifold type Artifact100021939.
- Sub-Riemannian_manifold type Conduit103089014.
- Sub-Riemannian_manifold type Manifold103717750.
- Sub-Riemannian_manifold type Object100002684.
- Sub-Riemannian_manifold type Passage103895293.
- Sub-Riemannian_manifold type PhysicalEntity100001930.
- Sub-Riemannian_manifold type Pipe103944672.
- Sub-Riemannian_manifold type RiemannianManifolds.
- Sub-Riemannian_manifold type Tube104493505.
- Sub-Riemannian_manifold type Way104564698.
- Sub-Riemannian_manifold type Whole100003553.
- Sub-Riemannian_manifold type YagoGeoEntity.
- Sub-Riemannian_manifold type YagoPermanentlyLocatedEntity.
- 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 label "Variedad subriemanniana".
- Sub-Riemannian_manifold sameAs Variedad_subriemanniana.
- Sub-Riemannian_manifold sameAs m.03s1ff.
- Sub-Riemannian_manifold sameAs Q7630587.
- Sub-Riemannian_manifold sameAs Q7630587.
- Sub-Riemannian_manifold sameAs Sub-Riemannian_manifold.
- Sub-Riemannian_manifold wasDerivedFrom Sub-Riemannian_manifold?oldid=594191761.
- Sub-Riemannian_manifold isPrimaryTopicOf Sub-Riemannian_manifold.