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arXiv · 1309.4759

Generalized twistor spaces for hyperkähler manifolds

Rebecca Glover·Justin Sawon
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Abstract

Let M be a hyperkähler manifold. The S^2-family of complex structures compatible with the hyperkähler metric can be assembled into a single complex structure on Z=MxS^2; the resulting complex manifold is known as the twistor space of M. We describe the analogous construction for generalized complex structures in the sense of Hitchin. Specifically, we exhibit a natural S^2xS^2-family of generalized complex structures compatible with the hyperkähler metric, and assemble them into a single generalized complex structure on X=MxS^2xS^2. We call the resulting generalized complex manifold the generalized twistor space of M.

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Rebecca Glover, Justin Sawon. 2013-09-18. Generalized twistor spaces for hyperkähler manifolds. https://doi.org/10.1112/jlms%2Fjdu074

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