Matches in DBpedia 2014 for { <http://dbpedia.org/resource/Unit_tangent_bundle> ?p ?o. }
Showing items 1 to 27 of
27
with 100 items per page.
- Unit_tangent_bundle abstract "In Riemannian geometry, a branch of mathematics, the unit tangent bundle of a Riemannian manifold (M, g), denoted by UT(M) or simply UTM, is the unit sphere bundle for the tangent bundle T(M). It is a fiber bundle over M whose fiber at each point is the unit sphere in the tangent bundle:where Tx(M) denotes the tangent space to M at x. Thus, elements of UT(M) are pairs (x, v), where x is some point of the manifold and v is some tangent direction (of unit length) to the manifold at x. The unit tangent bundle is equipped with a natural projectionwhich takes each point of the bundle to its base point. The fiber π−1(x) over each point x ∈ M is an (n−1)-sphere Sn−1, where n is the dimension of M. The unit tangent bundle is therefore a sphere bundle over M with fiber Sn−1.The definition of unit sphere bundle can easily accommodate Finsler manifolds as well. Specifically, if M is a manifold equipped with a Finsler metric F : TM → R, then the unit sphere bundle is the subbundle of the tangent bundle whose fiber at x is the indicatrix of F:If M is an infinite-dimensional manifold (for example, a Banach, Fréchet or Hilbert manifold), then UT(M) can still be thought of as the unit sphere bundle for the tangent bundle T(M), but the fiber π−1(x) over x is then the infinite-dimensional unit sphere in the tangent space.".
- Unit_tangent_bundle wikiPageID "7932644".
- Unit_tangent_bundle wikiPageRevisionID "348382433".
- Unit_tangent_bundle hasPhotoCollection Unit_tangent_bundle.
- Unit_tangent_bundle subject Category:Differential_topology.
- Unit_tangent_bundle subject Category:Ergodic_theory.
- Unit_tangent_bundle subject Category:Fiber_bundles.
- Unit_tangent_bundle subject Category:Riemannian_geometry.
- Unit_tangent_bundle type AnimalTissue105267548.
- Unit_tangent_bundle type BodyPart105220461.
- Unit_tangent_bundle type FiberBundle105475681.
- Unit_tangent_bundle type FiberBundles.
- Unit_tangent_bundle type NervousTissue105296775.
- Unit_tangent_bundle type Part109385911.
- Unit_tangent_bundle type PhysicalEntity100001930.
- Unit_tangent_bundle type Thing100002452.
- Unit_tangent_bundle type Tissue105267345.
- Unit_tangent_bundle comment "In Riemannian geometry, a branch of mathematics, the unit tangent bundle of a Riemannian manifold (M, g), denoted by UT(M) or simply UTM, is the unit sphere bundle for the tangent bundle T(M). It is a fiber bundle over M whose fiber at each point is the unit sphere in the tangent bundle:where Tx(M) denotes the tangent space to M at x. Thus, elements of UT(M) are pairs (x, v), where x is some point of the manifold and v is some tangent direction (of unit length) to the manifold at x.".
- Unit_tangent_bundle label "Einheits-Tangentialbündel".
- Unit_tangent_bundle label "Unit tangent bundle".
- Unit_tangent_bundle sameAs Einheits-Tangentialbündel.
- Unit_tangent_bundle sameAs m.026kjn8.
- Unit_tangent_bundle sameAs Q7887158.
- Unit_tangent_bundle sameAs Q7887158.
- Unit_tangent_bundle sameAs Unit_tangent_bundle.
- Unit_tangent_bundle wasDerivedFrom Unit_tangent_bundle?oldid=348382433.
- Unit_tangent_bundle isPrimaryTopicOf Unit_tangent_bundle.