Complex Differential Geometry

小行星9703884 这个项目是在复杂的微分几何领域。这位研究者先前证明了非正曲紧致卡勒曲面的两个陈数之比总是在2和3之间;他现在希望将这项工作推广到更高维的情况。此外，研究人员将继续进行著名的Kodaira-Enriques复杂表面分类中的剩余分类。最后，研究者想构造一类非正弯曲的Kahler流形。 Kahler流形是曲面的推广，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。卡勒流形在数学的其他部分以及理论物理中也有应用。例如，宇宙弦模型中著名的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.