Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Connection_form> ?p ?o }
- Connection_form abstract "In mathematics, and specifically differential geometry, a connection form is a manner of organizing the data of a connection using the language of moving frames and differential forms.Historically, connection forms were introduced by Élie Cartan in the first half of the 20th century as part of, and one of the principal motivations for, his method of moving frames. The connection form generally depends on a choice of frame, and so is not a tensorial object. Various generalizations and reinterpretations of the connection form were formulated subsequent to Cartan's initial work. In particular, on a principal bundle, a principal connection is a natural reinterpretation of the connection form as a tensorial object. On the other hand, the connection form has the advantage that it is a differential form defined on the differentiable manifold, rather than on an abstract principal bundle over it. Hence, despite their lack of tensoriality, connection forms continue to be used because of the relative ease of performing calculations with them. In physics, connection forms are also used broadly in the context of gauge theory, through the gauge covariant derivative.A connection form associates to each basis of a vector bundle a matrix of differential forms. The connection form is not tensorial because under a change of basis, the connection form transforms in a manner that involves the exterior derivative of the transition functions, in much the same way as the Christoffel symbols for the Levi-Civita connection. The main tensorial invariant of a connection form is its curvature form. In the presence of a solder form identifying the vector bundle with the tangent bundle, there is an additional invariant: the torsion form. In many cases, connection forms are considered on vector bundles with additional structure: that of a fiber bundle with a structure group.".
- Connection_form wikiPageID "706412".
- Connection_form wikiPageLength "23858".
- Connection_form wikiPageOutDegree "92".
- Connection_form wikiPageRevisionID "650016142".
- Connection_form wikiPageWikiLink Adjoint_representation.
- Connection_form wikiPageWikiLink Affine_connection.
- Connection_form wikiPageWikiLink Almost_complex_manifold.
- Connection_form wikiPageWikiLink Associated_bundle.
- Connection_form wikiPageWikiLink Atlas_(topology).
- Connection_form wikiPageWikiLink Basis_(linear_algebra).
- Connection_form wikiPageWikiLink Basis_of_a_vector_space.
- Connection_form wikiPageWikiLink CR_manifold.
- Connection_form wikiPageWikiLink Cartan_connection.
- Connection_form wikiPageWikiLink Category:Connection_(mathematics).
- Connection_form wikiPageWikiLink Category:Differential_geometry.
- Connection_form wikiPageWikiLink Category:Fiber_bundles.
- Connection_form wikiPageWikiLink Chain_complex.
- Connection_form wikiPageWikiLink Change_of_basis.
- Connection_form wikiPageWikiLink Charles_Ehresmann.
- Connection_form wikiPageWikiLink Christoffel_symbols.
- Connection_form wikiPageWikiLink Closed_and_exact_differential_forms.
- Connection_form wikiPageWikiLink Complex_manifold.
- Connection_form wikiPageWikiLink Connection_(mathematics).
- Connection_form wikiPageWikiLink Connection_(principal_bundle).
- Connection_form wikiPageWikiLink Connection_(vector_bundle).
- Connection_form wikiPageWikiLink Cotangent_bundle.
- Connection_form wikiPageWikiLink Covariance_and_contravariance_of_vectors.
- Connection_form wikiPageWikiLink Curvature_form.
- Connection_form wikiPageWikiLink De_Rham_cohomology.
- Connection_form wikiPageWikiLink Derivation_(abstract_algebra).
- Connection_form wikiPageWikiLink Derivation_(differential_algebra).
- Connection_form wikiPageWikiLink Differentiable_manifold.
- Connection_form wikiPageWikiLink Differential_form.
- Connection_form wikiPageWikiLink Differential_geometry.
- Connection_form wikiPageWikiLink Differential_operator.
- Connection_form wikiPageWikiLink Dual_basis.
- Connection_form wikiPageWikiLink Ehresmann_connection.
- Connection_form wikiPageWikiLink Einstein_notation.
- Connection_form wikiPageWikiLink Endomorphism_ring.
- Connection_form wikiPageWikiLink Equivalence_relation.
- Connection_form wikiPageWikiLink Exterior_algebra.
- Connection_form wikiPageWikiLink Exterior_derivative.
- Connection_form wikiPageWikiLink Fiber_bundle.
- Connection_form wikiPageWikiLink Fibre_bundle.
- Connection_form wikiPageWikiLink Foundations_of_Differential_Geometry.
- Connection_form wikiPageWikiLink Gauge_covariant_derivative.
- Connection_form wikiPageWikiLink Gauge_theory.
- Connection_form wikiPageWikiLink Hermitian_manifold.
- Connection_form wikiPageWikiLink Hermitian_metric.
- Connection_form wikiPageWikiLink Holonomic_basis.
- Connection_form wikiPageWikiLink Kronecker_delta.
- Connection_form wikiPageWikiLink Levi-Civita_connection.
- Connection_form wikiPageWikiLink Lie_algebra.
- Connection_form wikiPageWikiLink Lie_group.
- Connection_form wikiPageWikiLink Mathematics.
- Connection_form wikiPageWikiLink Matrix_(mathematics).
- Connection_form wikiPageWikiLink Maurer-Cartan_form.
- Connection_form wikiPageWikiLink Maurer–Cartan_form.
- Connection_form wikiPageWikiLink Metric_(vector_bundle).
- Connection_form wikiPageWikiLink Metric_compatible.
- Connection_form wikiPageWikiLink Metric_connection.
- Connection_form wikiPageWikiLink Moving_frame.
- Connection_form wikiPageWikiLink One-form.
- Connection_form wikiPageWikiLink Orthogonal_group.
- Connection_form wikiPageWikiLink Orthonormal_basis.
- Connection_form wikiPageWikiLink Parallel_transport.
- Connection_form wikiPageWikiLink Physics.
- Connection_form wikiPageWikiLink Poincaré_lemma.
- Connection_form wikiPageWikiLink Principal_bundle.
- Connection_form wikiPageWikiLink Pullback_(differential_geometry).
- Connection_form wikiPageWikiLink Pushforward_(differential).
- Connection_form wikiPageWikiLink Riemann_curvature_tensor.
- Connection_form wikiPageWikiLink Riemannian_manifold.
- Connection_form wikiPageWikiLink Riemannian_metric.
- Connection_form wikiPageWikiLink Section_(fiber_bundle).
- Connection_form wikiPageWikiLink Section_(fibre_bundle).
- Connection_form wikiPageWikiLink Sheaf_(mathematics).
- Connection_form wikiPageWikiLink Solder_form.
- Connection_form wikiPageWikiLink Spin_group.
- Connection_form wikiPageWikiLink Spin_structure.
- Connection_form wikiPageWikiLink Spinor.
- Connection_form wikiPageWikiLink Summation_convention.
- Connection_form wikiPageWikiLink Tangent_bundle.
- Connection_form wikiPageWikiLink Tensor.
- Connection_form wikiPageWikiLink Torsion_(differential_geometry).
- Connection_form wikiPageWikiLink Torsion_tensor.
- Connection_form wikiPageWikiLink Unitary_group.
- Connection_form wikiPageWikiLink Vector-valued_differential_form.
- Connection_form wikiPageWikiLink Vector-valued_form.
- Connection_form wikiPageWikiLink Vector_bundle.
- Connection_form wikiPageWikiLink Élie_Cartan.
- Connection_form wikiPageWikiLinkText "Connection form".
- Connection_form wikiPageWikiLinkText "Connection".
- Connection_form wikiPageWikiLinkText "Exterior connections".
- Connection_form wikiPageWikiLinkText "connection form".
- Connection_form wikiPageWikiLinkText "connection".
- Connection_form wikiPageWikiLinkText "connections".
- Connection_form wikiPageWikiLinkText "torsion".
- Connection_form hasPhotoCollection Connection_form.