Topic
Generalized complex structure
About: Generalized complex structure is a research topic. Over the lifetime, 240 publications have been published within this topic receiving 8858 citations. The topic is also known as: generalized complex manifold.
Papers published on a yearly basis
Papers
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TL;DR: In this paper, the concept of a generalized Kahler manifold has been introduced, which is equivalent to a bi-Hermitian geometry with torsion first discovered by physicists.
Abstract: Generalized complex geometry, as developed by Hitchin, contains complex and symplectic geometry as its extremal special cases. In this thesis, we explore novel phenomena exhibited by this geometry, such as the natural action of a B-field. We provide new examples, including some on manifolds admitting no known complex or symplectic structure. We prove a generalized Darboux theorem which yields a local normal form for the geometry. We show that there is an elliptic deformation theory and establish the existence of a Kuranishi moduli space.
We then define the concept of a generalized Kahler manifold. We prove that generalized Kahler geometry is equivalent to a bi-Hermitian geometry with torsion first discovered by physicists. We then use this result to solve an outstanding problem in 4-dimensional bi-Hermitian geometry: we prove that there exists a Riemannian metric on the complex projective plane which admits exactly two distinct Hermitian complex structures with equal orientation.
Finally, we introduce the concept of generalized complex submanifold, and show that such sub-objects correspond to D-branes in the topological A- and B-models of string theory.
1,444 citations
TL;DR: Generalized complex geometry encompasses complex and symplectic ge- ometry as its extremal special cases as mentioned in this paper, including generalized complex branes, which interpolate be- tween at bundles on Lagrangian submanifolds and holomorphic bundles on complex sub-mansifolds, and the basic properties of this geometry, including its enhanced symmetry group, elliptic deforma- tion theory, relation to Poisson geometry, and local structure theory.
Abstract: Generalized complex geometry encompasses complex and symplectic ge- ometry as its extremal special cases. We explore the basic properties of this geometry, including its enhanced symmetry group, elliptic deforma- tion theory, relation to Poisson geometry, and local structure theory. We also dene and study generalized complex branes, which interpolate be- tween at bundles on Lagrangian submanifolds and holomorphic bundles on complex submanifolds.
1,350 citations
TL;DR: In this paper, the twisted chiral multiplet is used to formulate supersymmetric nonlinear σ-models with N = 2,4 extended supersymmetry, which fall outside the classification given by Alvarez-Gaume and Freedman.
1,091 citations
TL;DR: A manifold is called a complex manifold if it can be covered by coordinate patches with complex coordinates in which the coordinates in overlapping patches are related by complex analytic transformations as mentioned in this paper, and a manifold can be called almost complex if there is a linear transformation J defined on the tangent space at every point, and varying differentiably with respect to local coordinates.
Abstract: A manifold is called a complex manifold if it can be covered by coordinate patches with complex coordinates in which the coordinates in overlapping patches are related by complex analytic transformations. On such a manifold scalar multiplication by i in the tangent space has an invariant meaning. An even dimensional 2n real manifold is called almost complex if there is a linear transformation J defined on the tangent space at every point (and varying differentiably with respect to local coordinates) whose square is minus the identity, i.e. if there is a real tensor field h' satisfying
869 citations
TL;DR: In this paper, a modification of Poisson geometry by a closed 3-form is studied. But the authors focus on twisted Poisson structures, which can be seen as glued from ordinary Poisson structure defined on local patches.
Abstract: We study a modification of Poisson geometry by a closed 3-form. Just as for ordinary Poisson structures, these "twisted" Poisson structures are conveniently described as Dirac structures in suitable Courant algebroids. The additive group of 2-forms acts on twisted Poisson structures and permits them to be seen as glued from ordinary Poisson structures defined on local patches. We conclude with remarks on deformation quantization and twisted symplectic groupoids.
535 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 7 |
| 2020 | 6 |
| 2019 | 3 |
| 2018 | 7 |
| 2017 | 10 |
| 2016 | 11 |