Classification of indefinite hyper-Kaehler symmetric spaces

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

We classify indefinite simply connected hyper-Kaehler symmetric spaces. Any such space without flat factor has commutative holonomy group and signature (4m,4m). We establish a natural 1-1 correspondence between simply connected hyper-Kaehler symmetric spaces of dimension 8m and orbits of the general linear group GL(m,H) over the quaternions on the space (S^4C^n)^τ of homogeneous quartic polynomials S in n = 2m complex variables satisfying the reality condition S = τS, where τis the real structure induced by the quaternionic structure of C^{2m} = H^m. We define and classify also complex hyper-Kaehler symmetric spaces. Such spaces without flat factor exist in any (complex) dimension divisible by 4.
28 pages, Latex

Keywords

Differential Geometry, 53C25, 53C35

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/59649

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0007189
 http://arxiv.org/abs/math/0007189

Collections

arXiv