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Hypercomplex manifolds with trivial canonical bundle and their holonomy

Misha Verbitsky
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Abstract

Let (M,I,J,K) be a compact hypercomplex manifold admitting an HKT-metric. Assume that the canonical bundle of (M,I) is trivial as a holomorphic line bundle. We show that the holonomy of Obata connection on M is contained in SL(n,H). In Appendix we apply these arguments to compact nilmanifolds equipped with abelian hypercomplex structures, showing that such manifolds have holonomy in SL(n,H).

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Misha Verbitsky. 2007-01-12. Hypercomplex manifolds with trivial canonical bundle and their holonomy. https://arxiv.org/abs/math/0406537

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