Geometric structures defined by differential forms (Calabi-Yau structures, generalized Kaeher structures)

我们得到了以下三个结果：(1)广义Kahler结构的构造和无阻碍变形：我们建立了广义Kahler结构的稳定性定理，并构造了许多有趣的例子。作为应用，我们证明了在具有非零全纯泊松结构的紧Kahler曲面上存在一个非平凡的比厄密结构。(2)利用对数变换构造广义复4流形的新方法：探索了应用任意对数变换的构造方法，得到了具有任意大量变型轨迹的有趣的广义复4流形。(3)广义Calabi-Yau度量和广义hyperKaehler结构的构造：

We obtain the following three results:(1) Constructions of generalized Kaehler structures and unobstructed deformations:We established the stability theorem of generalized Kahler structures and constructed many interesting examples. As an application, we showed that there exists a non-trivial bihermitian structure on compact Kahler surfaces with non-zero holomorphic Poisson structures.(2) New constructions of generalized complex 4-manifolds by logarithmic transformations:We explored the construction to apply arbitrary logarithmic transformations and obtain interesting generalized complex 4-manifods with arbitrary large number of type changing loci.(3) Constructions of generalized Calabi-Yau metrics and generalized hyperKaehler structures: