Hypercomplex structures associated to quaternionic manifolds

Henrik Pedersen Yat Sun Poon AF Swann

Complex Variables and Complex Analysis mathscidoc:1910.43797

Differential Geometry and its Applications, 9, (3), 273-292, 1998.12
If M is a quaternionic manifold and P is an S 1-instanton over M, then Joyce constructed a hypercomplex manifold we call(M) over M. These hypercomplex manifolds admit a U (2)-action of a special type permuting the complex structures. We show that up to double covers, all such hypercomplex manifolds arise in this way. Examples, including that of a hypercomplex structure on SU (3), show the necessity of including double covers of(M).
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@inproceedings{henrik1998hypercomplex,
  title={Hypercomplex structures associated to quaternionic manifolds},
  author={Henrik Pedersen, Yat Sun Poon, and AF Swann},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020220531794052326},
  booktitle={Differential Geometry and its Applications},
  volume={9},
  number={3},
  pages={273-292},
  year={1998},
}
Henrik Pedersen, Yat Sun Poon, and AF Swann. Hypercomplex structures associated to quaternionic manifolds. 1998. Vol. 9. In Differential Geometry and its Applications. pp.273-292. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020220531794052326.
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