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浙江大学学报（理学版）
浙江大学学报（理学版）  2016, Vol. 43 Issue (5): 537-538    DOI: 10.3785/j.issn.1008-9497.2016.05.007
数学与计算机科学     
双曲空间中全脐超曲面与高斯映照像
王琪
贵阳学院 数学与信息科学学院, 贵州 贵阳 550005
Totally umbilical hyper-surfaces of the hyperbolic space and the Gauss image
WANG Qi
School of Mathematics and Information Science, Guiyang University, Guiyang 550005, China
 全文: PDF(459 KB)  
摘要： 设Mn是单位双曲空间形式Hn+1中定向的紧致无边超曲面.假设存在整数r（1≤r≤n-1）使得高阶平均曲率Hi>0，i=1，2，…，r，且Hr是常数.证明了：如果Mn的高斯映照像包含在一个开半球面内，则Mn全脐.
关键词： 单位双曲空间形式;  全脐超曲面;  高斯映照像;  常数高阶平均曲率    
Abstract: Let Mn be a compact and oriented hyper-surface without boundary in the unit hyperbolic space form Hn+1. Assume that the i-mean curvature Hi>0,i=1,2,…,r for some integer r(1≤r≤n-1) and that Hr is constant, We proved that Mn is totally umbilical if the Gauss image of Mn is contained in an open hemisphere.
Key words: unit hyperbolic space form    totally umbilical hyper-surface    Gauss image    constant higher order mean curvature
收稿日期: 2015-11-16 出版日期: 2016-05-01
CLC:  O186.12  
基金资助: 贵州省科学技术基金项目（黔科合J字[2014]2005，黔科合LH字[2015]7298）.
作者简介: 王琪(1963-),ORCID:http://orcid.org/0000-0002-2921-6505,男,博士,教授,主要从事黎曼几何研究,E-mail:wangqihn@126.com.
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引用本文:

王琪. 双曲空间中全脐超曲面与高斯映照像[J]. 浙江大学学报（理学版）, 2016, 43(5): 537-538.

WANG Qi. Totally umbilical hyper-surfaces of the hyperbolic space and the Gauss image. Journal of ZheJIang University(Science Edition), 2016, 43(5): 537-538.

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https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2016.05.007    或    https://www.zjujournals.com/sci/CN/Y2016/V43/I5/537

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