Institute for Mathematical Physics Hypercomplex Structures Associated to Quaternionic Manifolds Hypercomplex Structures Associated to Quaternionic Manifolds
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چکیده
If M is a quaternionic manifold and P is an S 1-instanton over M , then Joyce constructed a hypercomplex manifold we call P (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 P (M).
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تاریخ انتشار 2009