Hypercomplex manifolds with trivial canonical bundle and their holonomy
نویسنده
چکیده
Let (M, I, J,K) be a compact hypercomplex manifold admitting a special kind of quaternionic-Hermitian metric called an HKT-metric. Assume that the canonical bundle of (M, I) is trivial as a holomorphic line bundle. We show that the holonomy of canonical torsion-free connection called Obata connection onM is contained in SL(n,H). In Appendix we apply these arguments to compact nilmanifolds which admit an abelian hypercomplex structuree, showing that such manifolds have holonomy in SL(n,H).
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تاریخ انتشار 2004