Rigidity of compact minimal submanifolds in a unit sphere
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LetM be ann-dimensional compact minimal submanifold of a unit sphereS n+p (p≥2); and letS be a square of the length of the second fundamental form. IfS≤2/3n everywhere onM, thenM must be totally geodesic or a Veronese surface.
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- Rigidity of compact minimal submanifolds in a unit sphere
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