  In this paper, we generalize the construction of Deligne-Hitchin twistor
space by gluing two certain Hodge moduli spaces. We investigate such
generalized Deligne-Hitchin twistor space as a complex analytic manifold. More
precisely, we show it admits holomorphic sections with weight-one property and
semi-negative energy, and it carries a balanced metric, and its holomorphic
tangent bundle (for the case of rank one) is stable. Moreover, we also study
the automorphism groups of the Hodge moduli spaces and the generalized
Deligne-Hitchin twistor space.
