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 Cliffo...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.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 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.
