New examples of indefinite hyper-Kaehler symmetric spaces

2005/03/11 by Ines Kath, Kath, Ines, Martin Olbrich +1 · 1 citation
Mathematics · Physics and Astronomy · #53C26 #53C35 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Representation Theory (math.RT) #math.DG #math.RT #msc:53C26 #msc:53C35

paper · pdf · doi:10.48550/arxiv.math/0503220

20 pages

arxiv created 2005/03/11 · openalex publication_date 2005/03/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Following the approach to pseudo-Riemannian symmetric spaces developed in math.DG/0408249 we exhibit examples of indefinite hyper-Kaehler symmetric spaces with non-abelian holonomy. Moreover, we classify indecomposable hyper-Kaehler symmetric spaces whose metric has signature (4,4n). Such spaces exist if and only if n=0,1,3.

Cited by

• The classification problem for pseudo-Riemannian symmetric spaces

Related

• Classification of indefinite hyper-Kaehler symmetric spaces
• Indefinite extrinsic symmetric spaces I
• Solvable Pseudo-Riemannian Symmetric Spaces
• Complex extensions of semisimple symmetric spaces
• Indefinite extrinsic symmetric spaces II