Generalized Complex Structure

(Differential Geometry)

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Differential Geometry
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What is 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 and . These structures first arose in Hitchin's program of characterizing geometrical structures via functionals of differential forms, a connection which formed the basis of Robbert Dijkgraaf, Sergei Gukov, and Cumrun Vafa's 2004 proposal that topological string theories are special cases of a topological M-theory. Today generalized complex structures also play a leading role in physical string theory, as supersymmetric flux compactifications, which relate 10-dimensional physics to 4-dimensional worlds like ours, require (possibly twisted) generalized complex structures.

Technology Types

differential geometrystructures on manifold

Synonyms

Generalized almost complex structureGeneralized Calabi-Yau manifoldGeneralized Calabi–Yau manifoldGeneralized complex geometryGeneralized complex manifold

Translations

일반화 복소다양체 (ko)一般化された複素構造 (ja)

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