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复空间形式中常数量曲率的完备全实伪脐子流形
引用本文:朱静勇,宋卫东.复空间形式中常数量曲率的完备全实伪脐子流形[J].纯粹数学与应用数学,2011,27(1):116-122.
作者姓名:朱静勇  宋卫东
作者单位:安徽师范大学数学计算机科学学院,安徽,芜湖,241000
基金项目:安徽省教育厅自然科学基金
摘    要:设CNnc是具有常全纯截面曲率c(≤O)的复n维的复空间形式,Mn是CNnc中常数量曲率的完备全实伪脐子流形,R,‖h‖2分别表示Mn的标准数量曲率和第二基本形式模长的平方.假设R≥c/4.利用丘成桐的广义极大值原理和自伴随算子研究了关于‖h‖2的pinching问题,得到了两个Mn成为全测地或全脐的刚性定理.

关 键 词:复空间形式  常数量曲率  伪脐  第二基本形式  全测地  全脐

Complete totally real pseudo-umbilical submanifolds with constant scalar curvature in a complex space form
ZHU Jing-yong,SONG Wei-dong.Complete totally real pseudo-umbilical submanifolds with constant scalar curvature in a complex space form[J].Pure and Applied Mathematics,2011,27(1):116-122.
Authors:ZHU Jing-yong  SONG Wei-dong
Institution:(College of Mathematics and Computer Science,Anhui Normal University,Wuhu 241000,China)
Abstract:Let CNcn be a complex space form,of complex dimension n,with constant holomorphic sectional curvature c(≤ 0).Mn is a complete totally real pseudo-umbilical submanifold with constant scalar curvaturein CNcn.Denoted by R and h 2,the normalized scalar curvature and the square of the length of the second fundamental form of Mn,respectively.Suppose R ≥ c/4.We studied the pinching problem on h 2 by making use of the generalized maximal principle and self-adjoint differential operator of Yau,and obtained two rigidity theorems for Mn to be a totally geodesic or totally umblilic submanifold.
Keywords:complex space form  constant scalar curvature  pseudo-umbilical  the second fundamental form  totally geodesic  totally umblilic
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