论文摘要
本文主要研究了Einstein流形及空间形式中的Einstein子流形的有关性质,得到了关于Einstein流形的一些结论和这类黎曼流形的几个Pinching定理,其主要结果如下:1.n（n4）维连通的Einstein流形（M,g）上存在12（n-1）（n-2）个截面,它们的截面曲率和为常数.2. 设M是n（n5）维具有平行李奇曲率张量场的黎曼流形,M不是Einstein流形,若它的所有Einstein子空间Mt满足dimMt4,则在M上处处成立3. 设M为S4内的紧致常中曲率Einstein超曲面且则必有R=0
论文目录
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标签：截面曲率论文; 平行论文; 李奇曲率论文; 超曲面论文; 局部对称空间论文; 积分公式论文; 平均曲率论文; 主曲率论文; 数量曲率论文; 第二基本形式论文; 共形平坦论文; 子空间论文; 向量场论文;