| 聂昌雄.共形空间${\mathbb Q}^n_s$中的正则Blaschke拟全脐子流形[J].数学年刊A辑,2015,36(1):59~68 |
| 共形空间${\mathbb Q}^n_s$中的正则Blaschke拟全脐子流形 |
| Regular Blaschke Quasi-umbilical Submanifolds in the Conformal Space ${\mathbb Q}^n_s$ |
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| DOI： |
| 中文关键词: 正则子流形, 共形不变量, Blaschke拟全脐子流形 |
| 英文关键词:Regular submanifolds, Conformal
invariants, Blaschke quasi-umbilical submanifolds |
| 基金项目:本文受到国家留学基金 (No.[2011]5025) 的资助. |
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| 中文摘要: |
| [Nie C X, Wu C X, Regular submanifolds in the conformal space ${\mathbb Q}^n_p$, {\it
Chin Ann Math}, 2012, 33B(5):695--714]中研究了共形空间${\mathbb Q}^n_s$中
的正则子流形, 并引入了共形空间${\mathbb Q}^n_s$中的子流形理论.
本文作者将分类共形空间${\mathbb Q}^n_s$中的Blaschke拟全脐子流形,
证明伪Riemann空间形式中具有常数量曲率和平行的平均曲率向量场的正则子流形是共形空间中的Blaschke拟全脐子流形;
反之, 共形空间中的Blaschke拟全脐子流形共形等价于伪Riemann空
间形式中具有常数量曲率和平行的平均曲率向量场的正则子流形.
这一结论可看作是共形空间${\mathbb Q}^n_s$中共形迷向子流形
分类定理的推广. |
| 英文摘要: |
| In [Nie C X, Wu C X, Regular submanifolds in the conformal space ${\mathbb Q}^n_p$, {\it Chin Ann Math}, 2012, 33B(5):695--714],
the authors studied the regular submanifolds in the conformal
space ${\mathbb Q}^n_s$ and introduced the submanifold theory
in the conformal space ${\mathbb Q}^n_s$.
This paper classifies the Blaschke
quasi-umbilical submanifolds in the conformal space ${\mathbb Q}^n_s$.
It is proved that regular submanifolds in pseudo-Riemann space forms with constant scalar curvature
and parallel mean curvature vector field are Blaschke quasi-umbilical submanifolds in
the conformal space, and that any Blaschke quasi-umbilical submanifold in the conformal space is conformal equivalent to a
regular submanifold with
constant scalar
curvature and parallel mean curvature vector field in pseudo-Riemann space forms.
These results may be regarded as an extension of the classification of the conformal
isotropic submanifolds in the conformal space ${\mathbb Q}^n_s$. |
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