Generalized twistor spaces for hyperkähler manifolds

الأصل · EN

Let M be a hyperkähler manifold. The S²-family of complex structures compatible with the hyperkähler metric can be assembled into a single complex structure on Z=MxS²; 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 S²xS²-family of generalized complex structures compatible with the hyperkähler metric, and assemble them into a single generalized complex structure on X=MxS²xS². We call the resulting generalized complex manifold the generalized twistor space of M.