Complex Differential Geometry

9703884郑本项目属于复杂微分几何领域。这位研究人员早些时候证明了非正曲线紧致Kahler曲面的两个陈氏数之比总是在2到3之间；他现在希望将这一工作推广到更高维的环境。此外，研究人员还将继续进行著名的Kodaira-Enrique复杂曲面分类中的剩余分类。最后，研究人员想要构造一类非正曲线Kahler流形。Kahler流形推广了曲面，并且基于复数。Kahler流形的Chern数是某些拓扑不变的整数，即它们是在流形的小变形下不变的量。Kahler流形在数学的其他部分以及理论物理中都有应用。例如，在宇宙弦模型中使用的著名的Yau-Calabi空间就是Kahler流形。

9703884 Zheng This project lies in the area of complex differential geometry. The investigator earlier showed that the ration of the two Chern numbers of a nonpositively curved compact Kahler surface is always between two and three; he now wishes to generalize that work to higher dimensional settings. In addition, the investigator is to pursue the remaining classification in the famous Kodaira-Enriques classification for complex surfaces. Finally, the investigator would like to construct a certain class of nonpositively curved Kahler manifolds. Kahler manifolds generalize curved surfaces, and are based on complex numbers. The Chern numbers of a Kahler manifold are certain integers that are topologically invariant, i.e., they are quantities that are unchanged under small deformation of the manifold. Kahler manifolds have found applications in other parts of mathematics as well as theoretical physics. For example, the famous Yau-Calabi spaces used in the string model of the universe are Kahler manifolds.