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- Courant_bracket abstract "In a field of mathematics known as differential geometry, the Courant bracket is a generalization of the Lie bracket from an operation on the tangent bundle to an operation on the direct sum of the tangent bundle and the vector bundle of p-forms. The case p = 1 was introduced by Theodore James Courant in his 1990 doctoral dissertation as a structure that bridges Poisson geometry and presymplectic geometry, based on work with his advisor Alan Weinstein. The twisted version of the Courant bracket was introduced in 2001 by Pavol Severa, and studied in collaboration with Weinstein. Today a complex version of the p=1 Courant bracket plays a central role in the field of generalized complex geometry, introduced by Nigel Hitchin in 2002. Closure under the Courant bracket is the integrability condition of a generalized almost complex structure.".
- Courant_bracket wikiPageExternalLink 0401221.
- Courant_bracket wikiPageID "6855275".
- Courant_bracket wikiPageLength "8050".
- Courant_bracket wikiPageOutDegree "68".
- Courant_bracket wikiPageRevisionID "622686729".
- Courant_bracket wikiPageWikiLink Alan_Weinstein.
- Courant_bracket wikiPageWikiLink Almost_complex_manifold.
- Courant_bracket wikiPageWikiLink Anchor_map.
- Courant_bracket wikiPageWikiLink Antisymmetric_relation.
- Courant_bracket wikiPageWikiLink Automorphism.
- Courant_bracket wikiPageWikiLink Category:Binary_operations.
- Courant_bracket wikiPageWikiLink Category:Differential_geometry.
- Courant_bracket wikiPageWikiLink Chern_class.
- Courant_bracket wikiPageWikiLink Circle_bundle.
- Courant_bracket wikiPageWikiLink Closed_and_exact_differential_forms.
- Courant_bracket wikiPageWikiLink Cohomology.
- Courant_bracket wikiPageWikiLink Compactification_(physics).
- Courant_bracket wikiPageWikiLink Complex_conjugate.
- Courant_bracket wikiPageWikiLink Complex_dimension.
- Courant_bracket wikiPageWikiLink Complex_manifold.
- Courant_bracket wikiPageWikiLink Complex_number.
- Courant_bracket wikiPageWikiLink Cotangent_bundle.
- Courant_bracket wikiPageWikiLink Courant_algebroid.
- Courant_bracket wikiPageWikiLink Courant_bracket.
- Courant_bracket wikiPageWikiLink Differential_form.
- Courant_bracket wikiPageWikiLink Differential_geometry.
- Courant_bracket wikiPageWikiLink Dirac_structure.
- Courant_bracket wikiPageWikiLink Direct_sum_of_vector_bundles.
- Courant_bracket wikiPageWikiLink Exact_form.
- Courant_bracket wikiPageWikiLink Exterior_algebra.
- Courant_bracket wikiPageWikiLink Exterior_derivative.
- Courant_bracket wikiPageWikiLink Fiber_bundle.
- Courant_bracket wikiPageWikiLink Foliation.
- Courant_bracket wikiPageWikiLink Generalized_complex_geometry.
- Courant_bracket wikiPageWikiLink Generalized_complex_structure.
- Courant_bracket wikiPageWikiLink Gerbe.
- Courant_bracket wikiPageWikiLink Inner_product.
- Courant_bracket wikiPageWikiLink Inner_product_space.
- Courant_bracket wikiPageWikiLink Integrability_condition.
- Courant_bracket wikiPageWikiLink Integrability_conditions_for_differential_systems.
- Courant_bracket wikiPageWikiLink Invariant_vector_field.
- Courant_bracket wikiPageWikiLink Irene_Dorfman.
- Courant_bracket wikiPageWikiLink Isotropic_quadratic_form.
- Courant_bracket wikiPageWikiLink Isotropic_subspace.
- Courant_bracket wikiPageWikiLink Jacobi_identity.
- Courant_bracket wikiPageWikiLink Jacobiator.
- Courant_bracket wikiPageWikiLink Kalb-Ramond_field.
- Courant_bracket wikiPageWikiLink Kalb–Ramond_field.
- Courant_bracket wikiPageWikiLink Kähler_manifold.
- Courant_bracket wikiPageWikiLink Leibniz_rule.
- Courant_bracket wikiPageWikiLink Leibnizs_rule.
- Courant_bracket wikiPageWikiLink Lie_algebroid.
- Courant_bracket wikiPageWikiLink Lie_derivative.
- Courant_bracket wikiPageWikiLink Linear_subspace.
- Courant_bracket wikiPageWikiLink Manifold.
- Courant_bracket wikiPageWikiLink Manifold_(mathematics).
- Courant_bracket wikiPageWikiLink Mathematics.
- Courant_bracket wikiPageWikiLink Nigel_Hitchin.
- Courant_bracket wikiPageWikiLink Nijenhuis_tensor.
- Courant_bracket wikiPageWikiLink Pavol_Severa.
- Courant_bracket wikiPageWikiLink Ping_Xu.
- Courant_bracket wikiPageWikiLink Poisson_manifold.
- Courant_bracket wikiPageWikiLink Principal_bundle.
- Courant_bracket wikiPageWikiLink Quadratic_form.
- Courant_bracket wikiPageWikiLink Riemann_curvature_tensor.
- Courant_bracket wikiPageWikiLink Signature_of_a_quadratic_form.
- Courant_bracket wikiPageWikiLink String_theory.
- Courant_bracket wikiPageWikiLink Symplectic_geometry.
- Courant_bracket wikiPageWikiLink Tangent_bundle.
- Courant_bracket wikiPageWikiLink Tensor_product.
- Courant_bracket wikiPageWikiLink Theodore_James_Courant.
- Courant_bracket wikiPageWikiLink Vector_bundle.
- Courant_bracket wikiPageWikiLink Vector_field.
- Courant_bracket wikiPageWikiLink Zhang-Ju_Liu.
- Courant_bracket wikiPageWikiLinkText "Courant bracket".
- Courant_bracket wikiPageWikiLinkText "Courant_bracket#Dorfman_bracket".
- Courant_bracket wikiPageWikiLinkText "Dorfman bracket".
- Courant_bracket hasPhotoCollection Courant_bracket.
- Courant_bracket subject Category:Binary_operations.
- Courant_bracket subject Category:Differential_geometry.
- Courant_bracket hypernym Generalization.
- Courant_bracket type Physic.
- Courant_bracket comment "In a field of mathematics known as differential geometry, the Courant bracket is a generalization of the Lie bracket from an operation on the tangent bundle to an operation on the direct sum of the tangent bundle and the vector bundle of p-forms. The case p = 1 was introduced by Theodore James Courant in his 1990 doctoral dissertation as a structure that bridges Poisson geometry and presymplectic geometry, based on work with his advisor Alan Weinstein.".
- Courant_bracket label "Courant bracket".
- Courant_bracket sameAs m.0gsryg.
- Courant_bracket sameAs Q5178095.
- Courant_bracket sameAs Q5178095.
- Courant_bracket wasDerivedFrom Courant_bracket?oldid=622686729.
- Courant_bracket isPrimaryTopicOf Courant_bracket.