摘要
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-Kahler 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-Kahler Calabi-Yau ■■-manifolds.
基金
supported by the National Natural Science Foundation of China(No.12061014).
