Preprint 22/2005

New examples of indefinite hyper-Kähler symmetric spaces

Ines Kath and Martin Olbrich

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Submission date: 17. Mar. 2005
Pages: 22
published in: Journal of geometry and physics, 57 (2007) 8, p. 1697-1711 
DOI number (of the published article): 10.1016/j.geomphys.2007.02.004
MSC-Numbers: 53C26, 53C35, 17B56, 53C50
Keywords and phrases: hyper-k\"ahler manifold, symmetric spaces
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Following the approach to pseudo-Riemannian symmetric spaces developed in a previous paper we exhibit examples of indefinite hyper-Kähler symmetric spaces with non-abelian holonomy. Moreover, we classify indecomposable hyper-Kähler symmetric spaces whose metric has signature (4,4n). Such spaces exist if and only if formula5.

18.10.2019, 02:12