Generalized pseudo Kaehler structures
arXiv:0909.2011 · doi:10.1007/s00220-011-1213-1
Abstract
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