Classification of indefinite hyper-Kaehler symmetric spaces
| dc.creator | Alekseevsky, Dmitri V. | |
| dc.creator | Cortes, Vicente | |
| dc.date | 2000-07-31 | |
| dc.date.accessioned | 2026-07-07T04:36:35Z | |
| dc.date.available | 2026-07-07T04:36:35Z | |
| dc.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. | |
| dc.description | 28 pages, Latex | |
| dc.identifier | https://arxiv.org/abs/math/0007189 | |
| dc.identifier | http://arxiv.org/abs/math/0007189 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59649 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C25, 53C35 | |
| dc.title | Classification of indefinite hyper-Kaehler symmetric spaces | |
| dc.type | text |