Abstract
Using Hodge theory and Banach fixed point theorem,Liu and Zhu developed a global method to deal with various problems in deformation theory.In this note,the authors generalize Liu-Zhu's method to treat two deformation problems for non-Kähler manifolds.They apply the ∂(∂)-Hodge theory to construct a deformation formula for(p,q)-forms of compact complex manifold under deformations,which can be used to study the Hodge number of complex manifold under deformations.In the second part of this note,by using the ∂∂-Hodge theory,they provide a simple proof of the unobstructed deformation theorem for the non-Kähler Calabi-Yau ∂(-∂)-manifolds.
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