Generalized reduction and pure spinors

Drummond, Thiago

doi:10.4310/jsg.2014.v12.n3.a2

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Generalized Holomorphic Structures From Generalized Kähler R...1

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“…The reduced generalized Kähler structure can be described conveniently in terms of pure spinors. We refer the interested reader to [5] for a detailed account of pure spinors in the setting of generalized reduction.…”

Section: Generalized Holomorphic Structures From Generalized Kähler R...mentioning

confidence: 99%

Metric reduction and generalized holomorphic structures

Wang

2018

Journal of Geometry and Physics

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In this paper, metric reduction in generalized geometry is investigated. We show how the Bismut connections on the quotient manifold are obtained from those on the original manifold. The result facilitates the analysis of generalized Kähler reduction, which motivates the concept of metric generalized principal bundles and our approach to construct a family of generalized holomorphic line bundles over CP 2 equipped with some non-trivial generalized Kähler structures.

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Section: Generalized Holomorphic Structures From Generalized Kähler R...mentioning

confidence: 99%

Metric reduction and generalized holomorphic structures

Wang

2018

Journal of Geometry and Physics

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Complex Dirac Structures: Invariants and Local Structure

Aguero

Rubio

2022

Commun. Math. Phys.

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We study complex Dirac structures, that is, Dirac structures in the complexified generalized tangent bundle. These include presymplectic foliations, transverse holomorphic structures, CR-related geometries and generalized complex structures. We introduce two invariants, the order and the (normalized) type. We show that, together with the real index, they allow us to obtain a pointwise classification of complex Dirac structures. For constant order, we prove the existence of an underlying real Dirac structure, which generalizes the Poisson structure associated to a generalized complex structure. For constant real index and order, we prove a splitting theorem, which gives a local description in terms of a presymplectic leaf and a small transversal.

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Generalized reduction and pure spinors

Cited by 2 publications

References 34 publications

Metric reduction and generalized holomorphic structures

Metric reduction and generalized holomorphic structures

Complex Dirac Structures: Invariants and Local Structure

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