空间形式中的完备子流形

张运涛

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

数学季刊 >

2016 , Vol. 31 >Issue 3: 298 - 306

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2016.03.008

空间形式中的完备子流形

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School of Mathematics and Statistics,Jiangsu Normal University

ZHANG Yun-tao(1972-), male, native of Linyi, Shandong, an associate professor of Jiangsu Normal University, Ph.D., engages in di®erential geometry.

收稿日期: 2015-06-10

网络出版日期: 2020-11-05

基金资助

Supported by the National Natural Science Foundation of China(11071206)； Supported by the PAPD of Jiangsu Higher Education Institutions；

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On Complete Submanifolds in Space Forms

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School of Mathematics and Statistics,Jiangsu Normal University

ZHANG Yun-tao(1972-), male, native of Linyi, Shandong, an associate professor of Jiangsu Normal University, Ph.D., engages in di®erential geometry.

Received date: 2015-06-10

Online published: 2020-11-05

Supported by

Supported by the National Natural Science Foundation of China(11071206)； Supported by the PAPD of Jiangsu Higher Education Institutions；

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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

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张运涛 . 空间形式中的完备子流形[J]. 数学季刊, 2016 , 31(3) : 298 -306 . DOI: 10.13371/j.cnki.chin.q.j.m.2016.03.008

Abstract

Key words： submanifolds; principle curvature; Ricci curvature

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