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- Linear_connection abstract "In the mathematical field of differential geometry, the term linear connection can refer to either of the following overlapping concepts: a connection on a vector bundle, often viewed as a differential operator (a Koszul connection or covariant derivative); a principal connection on the frame bundle of a manifold or the induced connection on any associated bundle — such a connection is equivalently given by a Cartan connection for the affine group of affine space, and is often called an affine connection.The two meanings overlap, for example, in the notion of a linear connection on the tangent bundle of a manifold.In older literature, the term linear connection is occasionally used for an Ehresmann connection or Cartan connection on an arbitrary fiber bundle, to emphasise that these connections are "linear in the horizontal direction" (i.e., the horizontal bundle is a vector subbundle of the tangent bundle of the fiber bundle), even if they are not "linear in the vertical (fiber) direction". However, connections which are not linear in this sense have received little attention outside the study of spray structures and Finsler geometry.".
- Linear_connection wikiPageID "5760393".
- Linear_connection wikiPageLength "1524".
- Linear_connection wikiPageOutDegree "18".
- Linear_connection wikiPageRevisionID "547421936".
- Linear_connection wikiPageWikiLink Affine_connection.
- Linear_connection wikiPageWikiLink Affine_group.
- Linear_connection wikiPageWikiLink Affine_space.
- Linear_connection wikiPageWikiLink Associated_bundle.
- Linear_connection wikiPageWikiLink Cartan_connection.
- Linear_connection wikiPageWikiLink Category:Connection_(mathematics).
- Linear_connection wikiPageWikiLink Connection_(principal_bundle).
- Linear_connection wikiPageWikiLink Connection_(vector_bundle).
- Linear_connection wikiPageWikiLink Covariant_derivative.
- Linear_connection wikiPageWikiLink Differential_geometry.
- Linear_connection wikiPageWikiLink Ehresmann_connection.
- Linear_connection wikiPageWikiLink Finsler_geometry.
- Linear_connection wikiPageWikiLink Finsler_manifold.
- Linear_connection wikiPageWikiLink Frame_bundle.
- Linear_connection wikiPageWikiLink Horizontal_bundle.
- Linear_connection wikiPageWikiLink Mathematical.
- Linear_connection wikiPageWikiLink Mathematics.
- Linear_connection wikiPageWikiLink Spray_(mathematics).
- Linear_connection wikiPageWikiLink Tangent_bundle.
- Linear_connection wikiPageWikiLinkText "Linear connection".
- Linear_connection hasPhotoCollection Linear_connection.
- Linear_connection wikiPageUsesTemplate Template:Mathematical_disambiguation.
- Linear_connection wikiPageUsesTemplate Template:Reflist.
- Linear_connection subject Category:Connection_(mathematics).
- Linear_connection type Page.
- Linear_connection comment "In the mathematical field of differential geometry, the term linear connection can refer to either of the following overlapping concepts: a connection on a vector bundle, often viewed as a differential operator (a Koszul connection or covariant derivative); a principal connection on the frame bundle of a manifold or the induced connection on any associated bundle — such a connection is equivalently given by a Cartan connection for the affine group of affine space, and is often called an affine connection.The two meanings overlap, for example, in the notion of a linear connection on the tangent bundle of a manifold.In older literature, the term linear connection is occasionally used for an Ehresmann connection or Cartan connection on an arbitrary fiber bundle, to emphasise that these connections are "linear in the horizontal direction" (i.e., the horizontal bundle is a vector subbundle of the tangent bundle of the fiber bundle), even if they are not "linear in the vertical (fiber) direction". ".
- Linear_connection label "Linear connection".
- Linear_connection sameAs Conexión_lineal.
- Linear_connection sameAs Q8349715.
- Linear_connection sameAs Q8349715.
- Linear_connection wasDerivedFrom Linear_connection?oldid=547421936.
- Linear_connection isPrimaryTopicOf Linear_connection.