Hypercomplex manifolds with trivial canonical bundle and their holonomy

Details Hypercomplex manifolds with trivial canonical bundle and their holonomy Hypercomplex manifolds with trivial canonical bundle and their holonomy

2004-06-25

arxiv.org/abs/math/0406537v2

Moscow Seminar on Mathematical Physics. II, 203--211, Amer. Math. Soc. Transl. Ser. 2, 221, 2007

Mathematics

Differential Geometry

14 pages, minor misprints corrected

Scientific paper

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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