空间形式中的完备子流形

doi:10.13371/j.cnki.chin.q.j.m.2016.03.008

数学季刊 ›› 2016, Vol. 31 ›› Issue (3): 298-306.doi: 10.13371/j.cnki.chin.q.j.m.2016.03.008

空间形式中的完备子流形

School of Mathematics and Statistics,Jiangsu Normal University

收稿日期:2015-06-10 出版日期:2016-09-30 发布日期:2020-11-05
作者简介:ZHANG Yun-tao(1972-), male, native of Linyi, Shandong, an associate professor of Jiangsu Normal University, Ph.D., engages in di®erential geometry.
基金资助:
Supported by the National Natural Science Foundation of China(11071206)； Supported by the PAPD of Jiangsu Higher Education Institutions；

On Complete Submanifolds in Space Forms

School of Mathematics and Statistics,Jiangsu Normal University

Received:2015-06-10 Online:2016-09-30 Published:2020-11-05
About author:ZHANG Yun-tao(1972-), male, native of Linyi, Shandong, an associate professor of Jiangsu Normal University, Ph.D., engages in di®erential geometry.
Supported by:
Supported by the National Natural Science Foundation of China(11071206)； Supported by the PAPD of Jiangsu Higher Education Institutions；

摘要/Abstract

摘要： Let Mⁿ be an n（n≥4）-dimensional compact oriented submanifold in the nonnegative space forms N^n+p（c） with S ≤ S（c,H）.Then Mⁿ is either homeomorphic to a standard n-dimensional sphere Sⁿ or isometric to a Clifford torus.We also prove that a2 xt-2compact oriented submanifold in any N^n+p（c） is diffeomorphic to a sphere if S ≤（n²H²）/（n-1）+2c.

关键词: submanifolds, principle curvature, Ricci curvature

Abstract: Let Mⁿ be an n（n≥4）-dimensional compact oriented submanifold in the nonnegative space forms N^n+p（c） with S ≤ S（c,H）.Then Mⁿ is either homeomorphic to a standard n-dimensional sphere Sⁿ or isometric to a Clifford torus.We also prove that a2 xt-2compact oriented submanifold in any N^n+p（c） is diffeomorphic to a sphere if S ≤（n²H²）/（n-1）+2c.

Key words: submanifolds, principle curvature, Ricci curvature

中图分类号:

O186.12

张运涛. 空间形式中的完备子流形[J]. 数学季刊, 2016, 31(3): 298-306.

ZHANG Yun-tao. On Complete Submanifolds in Space Forms[J]. Chinese Quarterly Journal of Mathematics, 2016, 31(3): 298-306.

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空间形式中的完备子流形

On Complete Submanifolds in Space Forms

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