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Generalized complex structure

In the field of mathematics known as differential geometry, a generalized complex structure is a property of a differential manifold that includes as special cases a complex structure and a symplectic structure. Generalized complex structures were introduced by Nigel Hitchin in 2002 and further developed by his students Marco Gualtieri and Gil Cavalcanti.

Products, Definition & Maximal isotropic subbundles

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Definition

Maximal isotropic subbundles

Canonical bundle

Local classification

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Relation to G-structures

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Generalized complex structure

Nodes91
Edges90
Triples26
Avg. degree1.98
Density0.021978
Components1

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Generalized complex structure

Top relations

related to Complex manifolds · 7
Generalized complex structure → In, Lambda, Restricting, The, Therefore, This, Thus
related to Local holomorphicity · 7
Generalized complex structure → B-field, However, In, Near, Poisson, The, Weinstein's
related to Relation to G-structures · 4
Generalized complex structure → G-structures, Some, The, Therefore
related to Darboux's theorem · 3
Generalized complex structure → B-field, Cartesian, Every
is a · 2
Generalized complex structure → generalized almost complex structure such that the space of smooth sections of L is closed under the Courant bracket, property of a differential manifold that includes as special cases a complex structure and a symplectic structure
related to Integrability and other structures · 2
Generalized complex structure → Calabi-Yau, If
related to Definition · 1
Generalized complex structure → Courant

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Important terminology

complex generalized displaystyle structure mathbf bundle almost structures subbundle mathbb oplus pure type otimes tangent isotropic spinor symplectic vector one

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Generalized complex structureis aproperty of a differential manifold that includes as special cases a complex structure and a symplectic structure0.90text
Generalized complex structureis ageneralized almost complex structure such that the space of smooth sections of L is closed under the Courant bracket0.90text
Generalized complex structurerelated to Complex manifoldsThe0.60section
Generalized complex structurerelated to Complex manifoldsLambda0.60section
Generalized complex structurerelated to Complex manifoldsThis0.60section
Generalized complex structurerelated to Complex manifoldsIn0.60section
Generalized complex structurerelated to Complex manifoldsThus0.60section
Generalized complex structurerelated to Complex manifoldsRestricting0.60section
Generalized complex structurerelated to Complex manifoldsTherefore0.60section
Generalized complex structurerelated to Darboux's theoremEvery0.60section
Generalized complex structurerelated to Darboux's theoremB-field0.60section
Generalized complex structurerelated to Darboux's theoremCartesian0.60section

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