| 摘要: |
| 本文主要研究了不能全含于开半球中的一些特殊曲面.利用Lr算子的相关性质,证明了对Sn+1中紧致r-极小超曲面,如果第二基本形式的秩rank (hij)> r,则其不全含在Sn+1的一个开半球中. |
| 关键词: 高阶极小超曲面 常平均曲率 高斯映射 半球 |
| DOI： |
| 分类号:O186 |
| 基金项目: |
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| THE DISCUSSION OF SOME SURFACES WHICH ARE NOT ALL CONTAINED IN A HEMISPHERE |
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ZHANG Wen-juan
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School of Mathematics, Yunnan Normal University, Kunming 650500, China
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| Abstract: |
| In this paper, we mainly study some special surfaces which are not all contained in an open hemisphere. By using properties of Lr operator, we prove that for a compact r-minimal hypersurface in Sn+1, if the rank of the second fundamental form rank(hij) > r then the hypersurface can not be contained in an open hemisphere of Sn+1. |
| Key words: higher order minimal hypersurface constant mean curvature Gauss map hemisphere |
