Instantons, Poisson Structures and Generalized Kähler Geometry

By N. Hitchin. 2005

186 citations recorded by the source corpus.

Using the idea of a generalized Kähler structure, we construct bihermitian metrics on CP2 and CP1×CP1, and show that any such structure on a compact 4-manifold M defines one on the moduli space of anti-self-dual connections on a fixed principal bundle over M. We highlight the role of holomorphic Poisson structures in all these constructions.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/de009227ccd945e24bb96d6646b6308f8fc6e039

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

1. D. Waldram
2. Anna Fino
3. Luigi Vezzoni
4. Shengda Hu
5. M. Gualtieri
6. P. P. Pacheco
7. N. Hitchin
8. J. Jordan

In Mathematical Physics

1. D. Waldram
2. Shengda Hu
3. M. Gualtieri
4. Anna Fino
5. N. Hitchin
6. P. P. Pacheco
7. Luigi Vezzoni
8. J. Jordan

Citations in the corpus

• Branes on Poisson varieties (2007, methodology): “This is consistent with Hitchin’s general observation [22] that [I, J]g−1 defines a holomorphic Poisson structure for both I and J, for any generalized Kähler structure.”
• Non-Kähler Calabi-Yau geometry and pluriclosed flow (2021, methodology): “The tensor σ was discovered by Pontecorvo-Hitchin [4, 48, 37], and was shown to be constant along a solution to generalized Kähler-Ricci flow in [33, Corollary 1.5].”
• Generalized Kähler Geometry (2010, methodology): “329 Introduction Generalized Kähler geometry is the natural Riemannian geometry associated to a generalized complex structure in the sense of Hitchin.”
• A correction to “Tamed symplectic forms and strong Kähler with torsion metrics” (2012, background): “SKT metrics have a central role in type II string theory, in two-dimensional supersymmetric σ-models (see [17, 40]) and they also have relations with generalized Kähler geometry (see for instance [1, 5, 14, 17, 22, 26]).”
• M-theory, exceptional generalised geometry and superpotentials (2008, background): “Type II string backgrounds in d dimensions which include non-trivial fluxes have a natural description in terms of Hitchin’s generalised geometry [1, 2, 3, 4], where the metric and NS–NS B-field are combined into a single geometrical object, transforming under O(d, d).”
• Hamiltonian Symmetries and Reduction in Generalized Geometry (2005, background): “In [24] Hitchin described an example of generalized Kähler reduction.”