Moraru, R. and Verbitski, M. (2010) Stable bundles on hypercomplex surfaces. Central European Journal of Mathematics, 8(2), pp. 327-337. (doi: 10.2478/s11533-010-0006-7)
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Publisher's URL: http://dx.doi.org/10.2478/s11533-010-0006-7
Abstract
A hypercomplex manifold is a manifold equipped with three complex structures I; J;K satisfying the quaternionic relations. Let M be a 4-dimensional compact smooth manifold equipped with a hypercomplex structure, and E be a vector bundle on M. We show that the moduli space of anti-self-dual connections on E is also hypercomplex, and admits a strong HKT metric. We also study manifolds with (4,4)-supersymmetry, that is, Riemannian manifolds equipped with a pair of strong HKT-structures that have opposite torsion. In the language of Hitchin’s and Gualtieri’s generalized complex geometry, (4,4)-manifolds are called ”generalized hyperkähler manifolds”. We show that the moduli space of anti-self-dual connections on M is a (4,4)-manifold if M is equipped with a (4,4)-structure.
| Item Type: | Articles |
|---|---|
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Verbitski, Dr Mikhail |
| Authors: | Moraru, R., and Verbitski, M. |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Journal Name: | Central European Journal of Mathematics |
| Publisher: | Versita |
| ISSN: | 1895-1074 |
| ISSN (Online): | 1644-3616 |
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