Einstein流形的共形刚性

论文摘要

本文研究了一个具有常纯量曲率的紧致黎曼流形（Mn,g）可共形形变到一个Einstein流形的条件,证明了如下结论:1、纯量曲率为非正的Einstein流形不能共形形变到另一个Einstein流形,也就是说有刚性.2、纯量曲率为正的黎曼流形可非等距的共形形变到一个Einstein流形的必要条件是max||Ric-R/ng||2>cnc（λ1-c）,其中cn=（n-2）2/n,c=R/n-1,λ1为关于度量g的Laplace算子的第一特征值.等号成立的充要条件是（Mn,g）,等距同胚于球Sn（r）（r=1/（?））.

论文目录

文章来源

类型: 硕士论文

作者: 马赛飞

导师: 郭震

关键词: 流形,共形流形,共形刚性

来源: 云南师范大学

年度: 2019

分类: 基础科学

专业: 数学

单位: 云南师范大学

分类号: O186.12

总页数: 24

文件大小: 1181K

下载量: 12

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