Complex Differential Geometry

[9703884]郑这个项目属于复杂微分几何领域。研究者早先证明了非正弯曲致密Kahler曲面的两个陈恩数之比总是在2到3之间；他现在希望将这项工作推广到更高维度的环境中。此外，研究者正在追求在著名的Kodaira-Enriques分类中对复杂表面的剩余分类。最后，研究者想构造一类非正弯曲的Kahler流形。Kahler流形推广曲面，并且基于复数。Kahler流形的chen数是拓扑不变的整数，即在流形的小变形下它们是不变的量。Kahler流形在数学和理论物理的其他领域也有应用。例如，宇宙弦模型中使用的著名的yu - 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.