First eigenvalue of submanifolds in Euclidean space.
An application of stress energy tensor to the vanishing theorem of differential forms.
Global pinching theorems of submanifolds in spheres.
Spacelike hypersurfaces in de Sitter space with constant higher-order mean curvature.
Global pinching theorems for minimal submanifolds in spheres
Let M be a compact submanifold with parallel mean curvature vector embedded in the unit sphere . By using the Sobolev inequalities of P. Li to get estimates for the norms of certain tensors related to the second fundamental form of M, we prove some rigidity theorems. Denote by H and the mean curvature and the norm of the square length of the second fundamental form of M. We show that there is a constant C such that if , then M is a minimal submanifold in the sphere with sectional curvature...
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