Generalized Calabi-Yau metric and Generalized Monge-Ampere equation

Abstract

In the neighborhood of a regular point, generalized Kahler geometry admits a description in terms of a single real function, the generalized Kahler potential. We study the local conditions for a generalized Kahler manifold to be a generalized Calabi-Yau manifold and we derive a non-linear PDE that the generalized Kahler potential has to satisfy for this to be true. This non-linear PDE can be understood as a generalization of the complex Monge-Ampere equation and its solutions give supergravity solutions with metric, dilaton and H-field.

26 pages

References in corpus (10)

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Cited by in corpus (9)

• Novel Branches of (0,2) Theories
• The generalized Kaehler geometry of N=(2,2) WZW-models
• Semichiral Fields on S^2 and Generalized Kähler Geometry
• Exact helicoidal and catenoidal solutions in Einstein-Maxwell theory
• Generalized Kähler Geometry in (2,1) superspace
• Generalized Kahler structures on group manifolds and T-duality
• M-Branes on Minimal Surfaces
• On canonical metrics of complex surfaces with split tangent and related geometric PDEs
• The parabolic split-type Monge-Ampere on split tangent bundle surfaces