Hypercomplex manifolds with trivial canonical bundle and their holonomy
Differential Geometry
2008-05-21 v2 Algebraic Geometry
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).
Cite
@article{arxiv.math/0406537,
title = {Hypercomplex manifolds with trivial canonical bundle and their holonomy},
author = {Misha Verbitsky},
journal= {arXiv preprint arXiv:math/0406537},
year = {2008}
}
Comments
14 pages, minor misprints corrected