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-Kähler structures in the strongly degenerate case. The local form and the holonomy of a pseudo-Kähler 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-Kähler and pseudo-quaternion Kähler manifolds.

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