| 摘要: |
| 本文研究了五维单位球面S^5中具有常数量曲率和零Gauss-Kronecker曲率的完备极小超曲面. 我们得到了一个刚性结果: 这类超曲面一定是全测地的, 即等距于四维单位球面S^4. 我们的结果推广了Cui[1]最近的关于闭超曲面的结果, 也可以看作强陈省身猜想的一个正面支撑. |
| 关键词: 完备极小超曲面 五维单位球面S^5 Omori-Yau极值原理 零Gauss-Kronecker曲率 常数量曲率 |
| DOI： |
| 分类号:O186.11 |
| 基金项目:四川省自然科学基金项目资助 |
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| COMPLETE MINIMAL HYPERSURFACES IN S^5 WITH CONSTANT SCALAR CURVATURE AND ZERO GAUSS-KRONECKER CURVATURE |
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ZHANG BO YUAN
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| Abstract: |
| This paper studies complete minimal hypersurfaces in the five-dimensional unit sphere S^5 with constant scalar curvature and vanishing Gauss-Kronecker curvature. We obtain a rigidity result: such hypersurfaces must be totally geodesic, that is, isometric to the four-dimensional unit sphere S^4. Our result extends a recent result by Cui[1] concerning closed hypersurfaces and can also be viewed as supporting evidence for the strong Chern conjecture. |
| Key words: complete minimal hypersurface 5-dimensional unit sphere S^5 Omori-Yau maximum principle zero Gauss-Kronecker curvature constant scalar curvature |
