On Complete Submanifolds in Space Forms

ZHANG Yun-tao

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

Chinese Quarterly Journal of Mathematics >

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

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

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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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

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ZHANG Yun-tao . On Complete Submanifolds in Space Forms[J]. Chinese Quarterly Journal of Mathematics, 2016 , 31(3) : 298 -306 . DOI: 10.13371/j.cnki.chin.q.j.m.2016.03.008

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