Integrable Complex Structures on Twistor Spaces

We introduce integrable complex structures on twistor spaces fibered over complex manifolds. We then show, in particular, that the twistor spaces associated to generalized Kahler, SKT and Calabi-Yau manifolds all naturally admit complex structures. In \cite{Gindi1} we use the holomorphic sections of twistor spaces to derive various results about the complex geometries of the base manifolds.