Title：Recent progress in cohomogeneity one K/"ahler Einstein metrics
Speaker：Guan Zhuang-Dan (University of California, Riverside)
Time：2018年3月19日（周一） 下午 16:00-17:00
Room：东区管理科研楼 数学科学学院1518室
Abstract：Although there are many known K/"ahler-Einstein manifolds, there is so far no very practical method to check a given compact Fano manifold to be K/"ahler-Einstein or not.This is also true for the K/"ahler metrics with constant scalar curvatures or Calabi extremal metrics. The situation for a cohomogeneity one metrics was completely resolved.For the type III case, it was solved in my dissertation in 1992. For the remain type I and II case, the existence is equivalent to the negativity of a topological integral.The type I case was published in 2011. Therefore, the problem is reduced to check the negativity for classes of Fano manifolds. Recently, we use computer to get some insight into a few classes of type I Fano manifolds. This work is a joint work with a group of students.