Two Applications of the ■■-Hodge Theory  

Two Applications of the-Hodge

作　　者：Dingchang WEI Shengmao ZHU 

机构地区：[1]Center of Mathematical Sciences,Zhejiang University,Hangzhou 310027,China [2]Department of Mathematics,Zhejiang Normal University,Jinhua 321004,Zhejiang,China

出　　处：《Chinese Annals of Mathematics,Series B》2024年第1期137-150,共14页数学年刊（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China(No.12061014).

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.

关 键 词：Complex structures Deformations (p q)-Forms Non-Kahler Calabi-Yaumanifolds 

分 类 号：O186.1[理学—数学]