Generalized pseudo Kaehler structures

Details Generalized pseudo Kaehler structures Generalized pseudo Kaehler structures

2009-09-10

arxiv.org/abs/0909.2011v4

Commun.Math.Phys.304:49-68,2011

Mathematics

Differential Geometry

28 pages, to appear in Comm. Math. Phys

Scientific paper

10.1007/s00220-011-1213-1

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.

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