Geometrtic structures defined by differential forms (Topological Calibrations)

（1）广义Kaehler结构的构造与无障碍变形建立了广义Kaehler结构的稳定性定理，并构造了许多有趣的例子。作为应用，我们证明了具有非零全纯Poisson结构的紧致Kahler曲面上存在非平凡的双厄米结构。(2)非紧Kahler流形上的Calabi-Yau结构我们证明了Einstein-Sasaki流形的锥为正规孤立奇点的可分解的每个Kahler类上存在Ricci平坦完备Kahler度量。

We obtain the following two results:(1) Constructions of generalized Kaehler structures and unobstructed deformationsWe established the stability theorem of generalized Kahler structure and constructed many interesting examples. As an application, we showed that there exists a non-trivial bihermitian structure on compact Kahler surface with non-zero holomorphic Poisson structure.(2) Calabi-Yau structures on non-compact Kahler manifoldsWe showed that there is a Ricci-flat complete kahler metric on each Kahler class of a crepant resolution of normal isolated singularity which is the cone of an Einstein-Sasaki manifold.