摘要
Let M^n be an n(n≥4)-dimensional compact oriented submanifold in the nonnegative space forms N^(n+p)(c) with S ≤ S(c,H).Then M^n is either homeomorphic to a standard n-dimensional sphere S^n 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 ≤(n^2H^2)/(n-1)+2c.
Let M^n be an n（n≥4）-dimensional compact oriented submanifold in the non- negative space forms N^n＋p（c） with S ≤ S（c,H）. Then M^n is either homeomorphic to a standard n-dimensional sphere S^n or isometric to a Clifford torus. We also prove that a compact oriented submanifold in any N^n＋p （c） is diffeomorphic to a sphere if S≤（n^2H^2）/（n-1）＋2c.
基金
Supported by the National Natural Science Foundation of China(11071206)
Supported by the PAPD of Jiangsu Higher Education Institutions
