Generalized Kahler geometry

Abstract

Generalized Kahler geometry is the natural analogue of Kahler geometry, in the context of generalized complex geometry. Just as we may require a complex structure to be compatible with a Riemannian metric in a way which gives rise to a symplectic form, we may require a generalized complex structure to be compatible with a metric so that it defines a second generalized complex structure. We explore the fundamental aspects of this geometry, including its equivalence with the bi-Hermitian geometry on the target of a 2-dimensional sigma model with (2,2) supersymmetry, as well as the relation to holomorphic Dirac geometry and the resulting derived deformation theory. We also explore the analogy between pre-quantum line bundles and gerbes in the context of generalized Kahler geometry.

45 pages

References in corpus (22)

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• Courant algebroids: Cohomology and Matched Pairs
• Poisson structures and generalized Kahler structures
• Grothendieck Groups of Poisson Vector Bundles
• Poisson geometry with a 3-form background
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• Generalized Kaehler manifolds with split tangent bundle
• Invariants of Lie algebroids

Cited by in corpus (22)

• Algebroids, Heterotic Moduli Spaces and the Strominger System
• Generalized Kahler Geometry and the Pluriclosed Flow
• Infinitesimal moduli for the Strominger system and Killing spinors in generalized geometry
• Generalized holomorphic bundles and the B-field action
• Canonical metrics on holomorphic Courant algebroids
• Cosmological Implications from O(D,D)
• Hodge theory and deformations of SKT manifolds
• The generalized Kaehler geometry of N=(2,2) WZW-models
• Blowing up generalized Kahler 4-manifolds
• Twistors and Bi-Hermitian Surfaces of Non-Kähler Type
• Gauge Transformation of Double Field Theory for Open String
• Integrable deformation of ${\mathbb{CP}}^n$ and generalised Kaehler geometry
• Dimensional Reduction of the Generalized DBI
• Topological G${}_2$ and Spin(7) strings at 1-loop from double complexes
• Aeppli and Bott-Chern cohomology for bi-generalized Hermitian manifolds and $d^{\prime }{d}^{\prime \prime }$-lemma
• On gauged linear sigma models with torsion
• Odd type generalized complex structures on 4-manifolds
• On a question of Vaisman concerning complex surfaces
• Some Results of Deformations on Compact $H$-twisted Generalized Calabi-Yau Manifolds
• From locally conformally Kähler to bi-Hermitian structures on non-Kähler complex surfaces
• Espaces de twisteurs des structures complexes généralisées
• Static SKT metrics on Lie groups