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

2012/07/24 by M. Castrillón López, López, M. Castrillón, I. Luján +1 · 1 citation
Mathematics · #53C30 #53C50 #53C55 #53C80 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53C30 #msc:53C50 #msc:53C55 #msc:53C80

paper · pdf · doi:10.48550/arxiv.1207.5637

30 pages; Corrected typos

arxiv created 2012/08/01 · arxiv updated 2012/08/03

Abstract

We study the class K₂+K₄ 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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• Homogeneous structures of linear type on ε-Kähler and ε-quaternion Kähler manifolds

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