Generalized Kähler Geometry
By M. Gualtieri. 2010
145 citations recorded by the source corpus.
Generalized Kähler geometry is the natural analogue of Kähler 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 prove that generalized Kähler geometry is equivalent to the bi-Hermitian geometry on the target of a 2-dimensional sigma model with (2, 2) supersymmetry. We also prove the existence of natural holomorphic Courant algebroids for each of the underlying complex structures, and that these split into a sum of transverse holomorphic Dirac structures. Finally, we explore the analogy between pre-quantum line bundles and gerbes in the context of generalized Kähler geometry.
Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/2abe5271900821a2b1b4d278020ff4918e27ba25
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Geometry and Topology
- Anna Fino
- Fabio Paradiso
- J. Jordan
- M. Garcia‐Fernandez
- Jeffrey Streets
- Luigi Vezzoni
- Fang Zheng
- Xiaokui Yang
In Mathematical Physics
In Statistical and Nonlinear Physics
Citations in the corpus
- Non-Kähler Calabi-Yau geometry and pluriclosed flow (2021, methodology): “Then, the triple (g, JL, JR) is a natural generalized Kähler structure on G [36].”
- Balanced Hermitian structures on almost abelian Lie algebras (2020, methodology): “SKT metrics have natural applications in type II string theory and 2-dimensional supersymmetric σ-models [33, 54] and are closely related to generalized Kähler structures [35, 36, 1, 26, 23].”