Abstract
Let M be a hyperkahler manifold. The S-2-family of complex structures compatible with the hyperkahler metric can be assembled into a single complex structure on Z = M x S-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-2 x S-2-family of generalized complex structures compatible with the hyperkahler metric, and assemble them into a single generalized complex structure on X = M x S-2 x S-2. We call the resulting generalized complex manifold the generalized twistor space of M.