The pinching of n-dimensional closed hypersurface Mwith constant mean curvature H in unit sphere S^(n+1)( 1) is considered. Let A = ∑i,j,k h(ijk)~2( λi+ nH)~2,B = ∑i,j,k h(ijk)~2( λi+ nH) ·( λj+...
The National Natural Science Foundation of China(No.10971029,11101078,11171064);the Natural Science Foundation of Jiangsu Province(No.BK2011583)
The Frenet-Serret formula is used to characterize the constant angle ruled surfaces in R3. When the surfaces are the tangent developmental and normal surfaces, that is, r(s, v) = tr(s) +v(cosα(s) . t(s) +s...
In this paper, a rigidity theorem of hypersurface in real space form will be given. In addition, we obtain rigidity theorems of submanifold in sphere which improve the result of Hou and Xu.