Let Mn be an n-dimensional compact minimal submanifolds in Sin（1）× R. We prove two pinching theorems by the Ricci curvature and the sectional curvature pinching conditions respectively. In fact, we characterize...Let Mn be an n-dimensional compact minimal submanifolds in Sin（1）× R. We prove two pinching theorems by the Ricci curvature and the sectional curvature pinching conditions respectively. In fact, we characterize the Clifford tori and Veronese submanifolds by our pinching conditions respectively.展开更多
We obtain an inequality in Sm×R and Hm×R which is similar to DDVV conjecture.As an application,we show that a minimal submanifold in H m×R with nonnegative scalar curvature must be a surface of the type...We obtain an inequality in Sm×R and Hm×R which is similar to DDVV conjecture.As an application,we show that a minimal submanifold in H m×R with nonnegative scalar curvature must be a surface of the type γ×R,where γ is a geodesic in H m.In addition,we get a pinching theorem in Sm×R.展开更多
基金supported by National Natural Science Foundation of China (Grant No.11271214)
文摘Let Mn be an n-dimensional compact minimal submanifolds in Sin（1）× R. We prove two pinching theorems by the Ricci curvature and the sectional curvature pinching conditions respectively. In fact, we characterize the Clifford tori and Veronese submanifolds by our pinching conditions respectively.
基金supported by National Natural Science Foundation of China (Grant No.10871149)Research Fund for the Doctoral Program of Higher Education of China (Grant No. 200804860046)
文摘We obtain an inequality in Sm×R and Hm×R which is similar to DDVV conjecture.As an application,we show that a minimal submanifold in H m×R with nonnegative scalar curvature must be a surface of the type γ×R,where γ is a geodesic in H m.In addition,we get a pinching theorem in Sm×R.
