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.
@article{bwmeta1.element.doi-10_2478_s11533-010-0006-7,
author = {Ruxandra Moraru and Misha Verbitsky},
title = {Stable bundles on hypercomplex surfaces},
journal = {Open Mathematics},
volume = {8},
year = {2010},
pages = {327-337},
zbl = {1204.53040},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-010-0006-7}
}
Ruxandra Moraru; Misha Verbitsky. Stable bundles on hypercomplex surfaces. Open Mathematics, Tome 8 (2010) pp. 327-337. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-010-0006-7/
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