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

Abstract

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.

30 pages; Corrected typos

References in corpus (2)

• Lorentzian homogeneous spaces admitting a homogeneous structure of type T1+T3
• Holonomy groups and special geometric structures of pseudo-Kählerian manifolds of index 2