Generalized Pseudo-Kähler Structures
Copyright policy )Generalized Pseudo-Kähler Structures
In the paper we consider pseudo bihermitian structures - a pair of complex structures compatible with a pseudo Riemannian metric. As in the positive definite case we establish its relations with generalized (pseudo) Kaehler geometry and holomorphic Poisson structures. We provide a list of compact complex surfaces which could admit such structure and also examples of bihermitian structures on some of them. We also consider a naturally defined null plane distribution on generalized pseudo Kaehler 4-manifold and show that under a mild restriction it determines an Engel structure.
28 pages, to appear in Comm. Math. Phys
- Bulgarian Academy of Sciences Bulgaria
- Institute of Mathematics and Informatics Bulgaria
- Florida International University United States
Mathematics - Differential Geometry, High Energy Physics - Theory, FOS: Physical sciences, pseudo-Riemannian metric, 53C55, pseudo-bi-Hermitian, Poisson manifolds; Poisson groupoids and algebroids, Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics, holomorphic Poisson structures, Differential Geometry (math.DG), High Energy Physics - Theory (hep-th), General geometric structures on manifolds (almost complex, almost product structures, etc.), FOS: Mathematics, Engel structure
Mathematics - Differential Geometry, High Energy Physics - Theory, FOS: Physical sciences, pseudo-Riemannian metric, 53C55, pseudo-bi-Hermitian, Poisson manifolds; Poisson groupoids and algebroids, Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics, holomorphic Poisson structures, Differential Geometry (math.DG), High Energy Physics - Theory (hep-th), General geometric structures on manifolds (almost complex, almost product structures, etc.), FOS: Mathematics, Engel structure
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