In this article, we prove that the Clifford torus S^1(√1-r^2)×^n-1(r) is the only closed hypersurface in the unit sphere S^n+1(1) with infinite fundamental group, which satisfy r^2≥(n-1)/n,RicM≤C_(H...In this article, we prove that the Clifford torus S^1(√1-r^2)×^n-1(r) is the only closed hypersurface in the unit sphere S^n+1(1) with infinite fundamental group, which satisfy r^2≥(n-1)/n,RicM≤C_(H),and S≤S+(H).Moreover, we give a characterization of Clifford torus S^1(√1-r^2)×^n-1(r) with r^2=2n(1+H^2)^-2(n-1)+nH^2+|H|√n^2H^2+4(n-1).展开更多
基金supported by the Foundation of XuzhouNormal University (08XLA02)the Education Department of Jiangsu Province (07KJB110115)
文摘In this article, we prove that the Clifford torus S^1(√1-r^2)×^n-1(r) is the only closed hypersurface in the unit sphere S^n+1(1) with infinite fundamental group, which satisfy r^2≥(n-1)/n,RicM≤C_(H),and S≤S+(H).Moreover, we give a characterization of Clifford torus S^1(√1-r^2)×^n-1(r) with r^2=2n(1+H^2)^-2(n-1)+nH^2+|H|√n^2H^2+4(n-1).