On Holomorphic Sections of Certain Hermitian Vector Bundles.
S. KOBAYASHI, H.H. WU (1970)
Mathematische Annalen
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S. KOBAYASHI, H.H. WU (1970)
Mathematische Annalen
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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...
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