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A characterization of Projectively Flat manifolds
A characterization of Projectively Flat manifolds
教师介绍

本讲教师:Simone Calamai
所属学科:理科
人  气:122

课程介绍
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.

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