, Volume 45, Issue 1, pp 83-88

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.