Matches in DBpedia 2016-04 for { <http://dbpedia.org/resource/Cartan_connection> ?p ?o }
- Cartan_connection abstract "In the mathematical field of differential geometry, a Cartan connection is a flexible generalization of the notion of an affine connection. It may also be regarded as a specialization of the general concept of a principal connection, in which the geometry of the principal bundle is tied to the geometry of the base manifold using a solder form. Cartan connections describe the geometry of manifolds modelled on homogeneous spaces.The theory of Cartan connections was developed by Élie Cartan, as part of (and a way of formulating) his method of moving frames (repère mobile). The main idea is to develop a suitable notion of the connection forms and curvature using moving frames adapted to the particular geometrical problem at hand. For instance, in relativity or Riemannian geometry, orthonormal frames are used to obtain a description of the Levi-Civita connection as a Cartan connection. For Lie groups, Maurer–Cartan frames are used to view the Maurer–Cartan form of the group as a Cartan connection.Cartan reformulated the differential geometry of (pseudo) Riemannian geometry, as well as the differential geometry of manifolds equipped with some non-metric structure, including Lie groups and homogeneous spaces. The term Cartan connection most often refers to Cartan's formulation of a (pseudo-)Riemannian, affine, projective, or conformal connection. Although these are the most commonly used Cartan connections, they are special cases of a more general concept.Cartan's approach seems at first to be coordinate dependent because of the choice of frames it involves. However, it is not, and the notion can be described precisely using the language of principal bundles. Cartan connections induce covariant derivatives and other differential operators on certain associated bundles, hence a notion of parallel transport. They have many applications in geometry and physics: see the method of moving frames, Cartan connection applications and Einstein–Cartan theory for some examples.".
- Cartan_connection wikiPageID "412272".
- Cartan_connection wikiPageLength "45212".
- Cartan_connection wikiPageOutDegree "146".
- Cartan_connection wikiPageRevisionID "646871559".
- Cartan_connection wikiPageWikiLink Affine_connection.
- Cartan_connection wikiPageWikiLink Affine_group.
- Cartan_connection wikiPageWikiLink Affine_space.
- Cartan_connection wikiPageWikiLink Associated_bundle.
- Cartan_connection wikiPageWikiLink Atlas_(topology).
- Cartan_connection wikiPageWikiLink Borel_subgroup.
- Cartan_connection wikiPageWikiLink Bundle_map.
- Cartan_connection wikiPageWikiLink CR_manifold.
- Cartan_connection wikiPageWikiLink Cartan_formalism_(physics).
- Cartan_connection wikiPageWikiLink Category:Connection_(mathematics).
- Cartan_connection wikiPageWikiLink Category:Differential_geometry.
- Cartan_connection wikiPageWikiLink Celestial_sphere.
- Cartan_connection wikiPageWikiLink Conformal_connection.
- Cartan_connection wikiPageWikiLink Conformal_geometry.
- Cartan_connection wikiPageWikiLink Connection_(principal_bundle).
- Cartan_connection wikiPageWikiLink Connection_(vector_bundle).
- Cartan_connection wikiPageWikiLink Connection_form.
- Cartan_connection wikiPageWikiLink Coordinate_system.
- Cartan_connection wikiPageWikiLink Cotangent_bundle.
- Cartan_connection wikiPageWikiLink Cotangent_space.
- Cartan_connection wikiPageWikiLink Curvature.
- Cartan_connection wikiPageWikiLink Derivative.
- Cartan_connection wikiPageWikiLink Development_(differential_geometry).
- Cartan_connection wikiPageWikiLink Differentiable_manifold.
- Cartan_connection wikiPageWikiLink Differential_form.
- Cartan_connection wikiPageWikiLink Differential_geometry.
- Cartan_connection wikiPageWikiLink Differential_operator.
- Cartan_connection wikiPageWikiLink Differential_topology.
- Cartan_connection wikiPageWikiLink Duke_Mathematical_Journal.
- Cartan_connection wikiPageWikiLink Ehresmann_connection.
- Cartan_connection wikiPageWikiLink Einstein–Cartan_theory.
- Cartan_connection wikiPageWikiLink Encyclopedia_of_Mathematics.
- Cartan_connection wikiPageWikiLink Equivalence_relation.
- Cartan_connection wikiPageWikiLink Erlangen_program.
- Cartan_connection wikiPageWikiLink Euclidean_geometry.
- Cartan_connection wikiPageWikiLink Euclidean_space.
- Cartan_connection wikiPageWikiLink Felix_Klein.
- Cartan_connection wikiPageWikiLink Fiber_bundle.
- Cartan_connection wikiPageWikiLink File:Model_space_development.svg.
- Cartan_connection wikiPageWikiLink Foundations_of_Differential_Geometry.
- Cartan_connection wikiPageWikiLink Frame_bundle.
- Cartan_connection wikiPageWikiLink G-structure.
- Cartan_connection wikiPageWikiLink Gauge_fixing.
- Cartan_connection wikiPageWikiLink Group_action.
- Cartan_connection wikiPageWikiLink Group_representation.
- Cartan_connection wikiPageWikiLink Homogeneous_space.
- Cartan_connection wikiPageWikiLink Integrability_conditions_for_differential_systems.
- Cartan_connection wikiPageWikiLink Integral.
- Cartan_connection wikiPageWikiLink Killing_form.
- Cartan_connection wikiPageWikiLink Klein_geometry.
- Cartan_connection wikiPageWikiLink Levi-Civita_connection.
- Cartan_connection wikiPageWikiLink Lie_algebra.
- Cartan_connection wikiPageWikiLink Lie_algebra-valued_differential_form.
- Cartan_connection wikiPageWikiLink Lie_group.
- Cartan_connection wikiPageWikiLink Lorentz_group.
- Cartan_connection wikiPageWikiLink Manifold.
- Cartan_connection wikiPageWikiLink Maurer–Cartan_form.
- Cartan_connection wikiPageWikiLink Mean_curvature.
- Cartan_connection wikiPageWikiLink Minkowski_space.
- Cartan_connection wikiPageWikiLink Moving_frame.
- Cartan_connection wikiPageWikiLink Neighbourhood_(mathematics).
- Cartan_connection wikiPageWikiLink Orthogonal_group.
- Cartan_connection wikiPageWikiLink Orthonormal_frame.
- Cartan_connection wikiPageWikiLink Parabolic_Lie_algebra.
- Cartan_connection wikiPageWikiLink Parallel_transport.
- Cartan_connection wikiPageWikiLink Principal_bundle.
- Cartan_connection wikiPageWikiLink Principal_homogeneous_space.
- Cartan_connection wikiPageWikiLink Projective_connection.
- Cartan_connection wikiPageWikiLink Pseudo-Riemannian_manifold.
- Cartan_connection wikiPageWikiLink Pseudogroup.
- Cartan_connection wikiPageWikiLink Pullback_(differential_geometry).
- Cartan_connection wikiPageWikiLink Quadric.
- Cartan_connection wikiPageWikiLink Quotient_space_(topology).
- Cartan_connection wikiPageWikiLink Reductive_Lie_algebra.
- Cartan_connection wikiPageWikiLink Riemannian_geometry.
- Cartan_connection wikiPageWikiLink Riemannian_manifold.
- Cartan_connection wikiPageWikiLink Rigid_transformation.
- Cartan_connection wikiPageWikiLink Semidirect_product.
- Cartan_connection wikiPageWikiLink Semisimple_Lie_algebra.
- Cartan_connection wikiPageWikiLink Solder_form.
- Cartan_connection wikiPageWikiLink Spin_group.
- Cartan_connection wikiPageWikiLink Split_octonion.
- Cartan_connection wikiPageWikiLink Tangent_bundle.
- Cartan_connection wikiPageWikiLink Tangent_vector.
- Cartan_connection wikiPageWikiLink Topological_group.
- Cartan_connection wikiPageWikiLink Vector-valued_differential_form.
- Cartan_connection wikiPageWikiLink Vertical_bundle.
- Cartan_connection wikiPageWikiLink Élie_Cartan.
- Cartan_connection wikiPageWikiLinkText "Cartan connection".
- Cartan_connection wikiPageWikiLinkText "Cartan".
- Cartan_connection wikiPageWikiLinkText "connections".
- Cartan_connection author "Ü. Lumiste".
- Cartan_connection id "a/a010950".
- Cartan_connection title "Affine connection".
- Cartan_connection wikiPageUsesTemplate Template:Arxiv.