| C∞ Compactness for Minimal Submanifolds in the Unit Sphere |
| Received:June 10, 2000 |
| Key Words:
minimal submanifold totally geodesic compactness theorem.
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| Fund Project:Supported by the National Natural Science Foundation of China (19971081) |
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| Abstract: |
| In this paper we study the C∞ compactness for minimal submanifolds in the unit sphere. We obtain two compactness theorems. As an application, we prove that there is a positive number δ(n), such that if the square of the length of the second fundamental form of a minimal subrnanifold in the unit sphere is less than 2/3n+δ(n), it must be totally geodesic or diffeomorphic to a Veronese surface. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2003.02.001 |
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