scholarly journals Deformation classes in generalized Kähler geometry

2020 ◽  
Vol 7 (1) ◽  
pp. 241-256
Author(s):  
Matthew Gibson ◽  
Jeffrey Streets
Keyword(s):  
Symmetry Group ◽  
Ricci Flow ◽  
Kahler Geometry ◽  
Poisson Tensor ◽  
Natural Extensions ◽  
Generalized Kähler Geometry ◽  
Kähler Structures

AbstractWe describe natural deformation classes of generalized Kähler structures using the Courant symmetry group, which determine natural extensions of the notions of Kähler class and Kähler cone to generalized Kähler geometry. We show that the generalized Kähler-Ricci flow preserves this generalized Kähler cone, and the underlying real Poisson tensor.

scholarly journals The nondegenerate generalized Kähler Calabi–Yau problem

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Vestislav Apostolov ◽  
Jeffrey Streets
Keyword(s):  
Weak Convergence ◽  
Ricci Flow ◽  
Kahler Geometry ◽  
Kähler Metrics ◽  
Hamiltonian Action ◽  
Deformation Spaces ◽  
Kahler Metrics ◽  
Generalized Kähler Geometry ◽  
Kähler Structures ◽  
The Given

Abstract We formulate a Calabi–Yau-type conjecture in generalized Kähler geometry, focusing on the case of nondegenerate Poisson structure. After defining natural Hamiltonian deformation spaces for generalized Kähler structures generalizing the notion of Kähler class, we conjecture unique solvability of Gualtieri’s Calabi–Yau equation within this class. We establish the uniqueness, and moreover show that all such solutions are actually hyper-Kähler metrics. We furthermore establish a GIT framework for this problem, interpreting solutions of this equation as zeroes of a moment map associated to a Hamiltonian action and finding a Kempf–Ness functional. Lastly we indicate the naturality of generalized Kähler–Ricci flow in this setting, showing that it evolves within the given Hamiltonian deformation class, and that the Kempf–Ness functional is monotone, so that the only possible fixed points for the flow are hyper-Kähler metrics. On a hyper-Kähler background, we establish global existence and weak convergence of the flow.

scholarly journals Hyper-Kähler geometry and semi-geostrophic theory

2009 ◽  
Vol 466 (2113) ◽  
pp. 195-211 ◽  
Author(s):  
Sylvain Delahaies ◽  
Ian Roulstone
Keyword(s):  
Fluid Dynamics ◽  
Geophysical Fluid Dynamics ◽  
Kahler Geometry ◽  
Geometric Properties ◽  
Geostrophic Flows ◽  
Kähler Structures ◽  
Monge Ampere

We use the formalism of Monge–Ampère operators to study the geometric properties of the Monge–Ampère equations arising in semi-geostrophic (SG) theory and related models of geophysical fluid dynamics. We show how Kähler and hyper-Kähler structures arise, and the Legendre duality arising in SG theory is generalized to other models of nearly geostrophic flows.

scholarly journals T-duality, quotients and generalized Kähler geometry

2008 ◽  
Vol 665 (5) ◽  
pp. 401-408 ◽  
Author(s):  
Willie Merrell ◽  
Diana Vaman
Keyword(s):  
Kahler Geometry ◽  
Generalized Kähler Geometry

scholarly journals Formality in generalized Kähler geometry

2007 ◽  
Vol 154 (6) ◽  
pp. 1119-1125 ◽  
Author(s):  
Gil R. Cavalcanti
Keyword(s):  
Kahler Geometry ◽  
Generalized Kähler Geometry

scholarly journals Generalized Kähler geometry and manifest Script N = (2,2) supersymmetric nonlinear sigma-models

2005 ◽  
Vol 2005 (07) ◽  
pp. 067-067 ◽  
Author(s):  
Ulf Lindström ◽  
Martin Rocek ◽  
Rikard von Unge ◽  
Maxim Zabzine
Keyword(s):  
Sigma Models ◽  
Kahler Geometry ◽  
Generalized Kähler Geometry ◽  
Nonlinear Sigma Models

scholarly journals The generalized Kähler geometry of N = (2, 2) WZW-models

2011 ◽  
Vol 2011 (12) ◽  
Author(s):  
Alexander Sevrin ◽  
Wieland Staessens ◽  
Dimitri Terryn
Keyword(s):  
Kahler Geometry ◽  
Generalized Kähler Geometry

scholarly journals A potential for generalized Kähler geometry

2010 ◽  
pp. 263-273 ◽  
Author(s):  
Ulf Lindström ◽  
Martin Roček ◽  
Rikard von Unge ◽  
Maxim Zabzine
Keyword(s):  
Kahler Geometry ◽  
Generalized Kähler Geometry

scholarly journals Gauged (2,2) sigma models and generalized Kähler geometry

2007 ◽  
Vol 2007 (12) ◽  
pp. 039-039 ◽  
Author(s):  
Willie Merrell ◽  
Leopoldo A. Pando Zayas ◽  
Diana Vaman
Keyword(s):  
Sigma Models ◽  
Kahler Geometry ◽  
Generalized Kähler Geometry

scholarly journals Generalized Kähler geometry and the pluriclosed flow

2012 ◽  
Vol 858 (2) ◽  
pp. 366-376 ◽  
Author(s):  
Jeffrey Streets ◽  
Gang Tian
Keyword(s):  
Kahler Geometry ◽  
Generalized Kähler Geometry
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