题  目：A characterization of Projectively Flat manifolds

报告人：Simone Calamai  (Universita di Firenze)

时  间：2018年6月4日 （周一）   下午16:00-17:00

地  点：五教  5205 

内容提要：

We define a partition of the space of projectively flat metrics in three classes according to the sign of the Chern scalar curvature; we show that the class of negative projectively flat metrics is empty, and that the class of positive projectively flat metrics consists precisely of locally conformally flat-Kaehler metrics on Hopf manifolds, explicitly characterized by Vaisman. If time allows, we review the known characterization and properties of zero projectively flat metrics. As applications, we make sharp a list of possible projectively flat metrics by Li, Yau, and Zheng; moreover we show that projectively flat astheno-Kaehler metrics are in fact Kaehler and globally conformally flat.