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 ...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.展开更多
基金Supported by the National Natural Science Foundation of China(11071206)Supported by the PAPD of Jiangsu Higher Education Institutions
文摘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.
