摘要
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.
We obtain an inequality in S^m×R and H^m×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 γis a geodesic in H^m. In addition, we get a pinching theorem in S^m × R.
作者
CHEN Qun 1,2 & CUI Qing 3,1,1 School of Mathematics and Statistics,Wuhan University,Wuhan 430079,China
2 International Center for Theoretical Physics,Trieste 34100,Italy
3 School of Mathematics,Southwest Jiaotong University,Chengdu 610031,China
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)
