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- Horizontal_bundle abstract "In mathematics, in the field of differential topology, givenπ:E→M,a smooth fiber bundle over a smooth manifold M, then the vertical bundle VE of E is the subbundle of the tangent bundle TE consisting of the vectors which are tangent to the fibers of E over M. A horizontal bundle is then a particular choice of a subbundle of TE which is complementary to VE, in other words provides a complementary subspace in each fiber.In full generality, the horizontal bundle concept is one way to formulate the notion of an Ehresmann connection on a fiber bundle. However, the concept is usually applied in more specific contexts.More precisely, if e ∈ E withπ(e)=x ∈ M,then the vertical space VeE at e is the tangent space Te(Ex) to the fiber Ex through e. A horizontal bundle then determines a horizontal space HeE such that TeE is the direct sum of VeE and HeE.If E is a principal G-bundle then the horizontal bundle is usually required to be G-invariant: see Connection (principal bundle) for further details. In particular, this is the case when E is the frame bundle, i.e., the set of all frames for the tangent spaces of the manifold, and G = GLn.".
- Horizontal_bundle wikiPageID "9978772".
- Horizontal_bundle wikiPageLength "1995".
- Horizontal_bundle wikiPageOutDegree "20".
- Horizontal_bundle wikiPageRevisionID "649432742".
- Horizontal_bundle wikiPageWikiLink Basis_(linear_algebra).
- Horizontal_bundle wikiPageWikiLink Category:Connection_(mathematics).
- Horizontal_bundle wikiPageWikiLink Category:Differential_geometry.
- Horizontal_bundle wikiPageWikiLink Category:Differential_topology.
- Horizontal_bundle wikiPageWikiLink Complementary_subspace.
- Horizontal_bundle wikiPageWikiLink Connection_(principal_bundle).
- Horizontal_bundle wikiPageWikiLink Differentiable_manifold.
- Horizontal_bundle wikiPageWikiLink Differential_topology.
- Horizontal_bundle wikiPageWikiLink Direct_sum_of_modules.
- Horizontal_bundle wikiPageWikiLink Direct_sum_of_vector_spaces.
- Horizontal_bundle wikiPageWikiLink Ehresmann_connection.
- Horizontal_bundle wikiPageWikiLink Fiber_bundle.
- Horizontal_bundle wikiPageWikiLink Foundations_of_Differential_Geometry.
- Horizontal_bundle wikiPageWikiLink Frame_bundle.
- Horizontal_bundle wikiPageWikiLink Horizontal_form.
- Horizontal_bundle wikiPageWikiLink John_Wiley_&_Sons.
- Horizontal_bundle wikiPageWikiLink Mathematics.
- Horizontal_bundle wikiPageWikiLink Ordered_basis.
- Horizontal_bundle wikiPageWikiLink Principal_bundle.
- Horizontal_bundle wikiPageWikiLink Smooth_manifold.
- Horizontal_bundle wikiPageWikiLink Tangent_bundle.
- Horizontal_bundle wikiPageWikiLink Vertical_bundle.
- Horizontal_bundle wikiPageWikiLink Wiley_Interscience.
- Horizontal_bundle wikiPageWikiLinkText "Horizontal bundle".
- Horizontal_bundle wikiPageWikiLinkText "horizontal bundle".
- Horizontal_bundle wikiPageWikiLinkText "horizontal distribution".
- Horizontal_bundle wikiPageWikiLinkText "horizontal subspace".
- Horizontal_bundle wikiPageWikiLinkText "horizontal".
- Horizontal_bundle hasPhotoCollection Horizontal_bundle.
- Horizontal_bundle wikiPageUsesTemplate Template:Cite_book.
- Horizontal_bundle wikiPageUsesTemplate Template:Differential-geometry-stub.
- Horizontal_bundle wikiPageUsesTemplate Template:Topology-stub.
- Horizontal_bundle subject Category:Connection_(mathematics).
- Horizontal_bundle subject Category:Differential_geometry.
- Horizontal_bundle subject Category:Differential_topology.
- Horizontal_bundle hypernym Subbundle.
- Horizontal_bundle type Physic.
- Horizontal_bundle comment "In mathematics, in the field of differential topology, givenπ:E→M,a smooth fiber bundle over a smooth manifold M, then the vertical bundle VE of E is the subbundle of the tangent bundle TE consisting of the vectors which are tangent to the fibers of E over M.".
- Horizontal_bundle label "Horizontal bundle".
- Horizontal_bundle sameAs m.02pyrpb.
- Horizontal_bundle sameAs Q5903551.
- Horizontal_bundle sameAs Q5903551.
- Horizontal_bundle sameAs 水平丛.
- Horizontal_bundle wasDerivedFrom Horizontal_bundle?oldid=649432742.
- Horizontal_bundle isPrimaryTopicOf Horizontal_bundle.