文献类型：期刊文献

中文题名：非定空间形式N_p^(n+p)(c)中常数量曲率的类空子流形

英文题名：Space-like submanifolds with constant scalar curvature in an indefinite space form N_p^(n+p)(c).

作者：宣满友[1]

机构：[1]绍兴文理学院数学系

年份：2002

卷号：29

期号：4

起止页码：373

中文期刊名：浙江大学学报：理学版

收录：CSTPCD、、Scopus、CSCD2011_2012、CSCD

语种：中文

中文关键词：类空子流形;常标准数量曲率;非定空间形式;全脐子流形;起曲面;刚性定理

外文关键词：constant normalized scalar curvature; indefinite space form; totally umbilical submanifold

中文摘要：利用一个类似于 CHENG等引进的微分算子的新微分算子□ α(α=n+ 1,… ,n+ p) ,得到了非定空间形式 Nn+ pp (c)中常数量曲率的紧致的类空子流形的一个刚性定理 :设 Mn 是非定空间形式 Nn+ pp (c)(p>1)中标准数量曲率 R为常数的 n维 (n>2 )紧致的类空子流形 ,且标准平均曲率向量关于法联络平行 ,如果 R=R- 1,- 1

外文摘要：By use of new differential operator □ α(α=n+1,...,n+p) similar to the one introduced by CHENG et al, a rigidity result for a compact space-like submanifold of constant scalar curvature in an indefinite space form N n+p p(c) is obtained: Let M n be an n-dimensional (n>2) compact space-like submanifold with constant normalized scalar curvature R in an indefinite space from N n+p p(c)(p>1) and the unit mean curvature vector is paralled with respect to the normal connection, if =R-1,-1<≤0 and the norm square |B| 2 of the second fundamental form of M n satisfies -n≤|B| 2≤C(,p,n), where C(,p,n) is one constant which depending only on , p and n, then |B| 2=-n and M n is a totally umbilical submanifold. The result is extended in CHENG(1977) and LI(1996) to the space-like submanifolds with constant scalar curvature in an indefinite space form. Since the condition'flat normal bundle' is omited, the present discussion has an advantage over the discussion in HOU(1998).