# Strongly degenerate homogeneous pseudo-Kähler structures of linear type and complex plane waves

We study the class $\mathcal{K}_{2}+\mathcal{K}_{4}$ of homogeneous pseudo-K\"ahler structures in the strongly degenerate case. The local form and the holonomy of a pseudo-K\"ahler manifold admitting such a structure is obtained, leading to a possible complex generalization of homogeneous plane waves. The same question is tackled in the case of pseudo-hyper-K\"ahler and pseudo-quaternion K\"ahler manifolds.

Article:
Strongly degenerate homogeneous pseudo-Kähler structures of linear type and complex plane waves
Authors:
M. Castrillón López, I. Luján
Journal:
ArXiv preprint
Year:
2012
URL:
http://arxiv.org/abs/1207.5637