| n维Anti-de Sitter空间中类空超曲面的类时Gauss像的奇点 |
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| 引用本文： | 刘海明,苗佳晶.n维Anti-de Sitter空间中类空超曲面的类时Gauss像的奇点[J].中国科学:数学,2010,40(8):813-826. |
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| 作者姓名： | 刘海明 苗佳晶 |
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| 作者单位： | 牡丹江师范学院数学系, 牡丹江157000 |
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| 基金项目： | 牡丹江师范学院科技青年项目（批准号：QY200904）资助项目 |
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| 摘 要： | 本文利用奇点理论研究了n维Anti-deSitter空间中的类空超曲面,介绍了类空超曲面的局部微分几何,定义了类时Anti-deSitterGauss像及Anti-deSitter高度函数,并进一步的利用Anti-deSitter高度函数族和流形间的切触理论研究了类时Anti-deSitterGauss像的几何意义及类空超曲面的通有性.最后研究了类空超曲面的AdS-Monge型.
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| 关 键 词： | n维 Anti-de Sitter空间 类空超曲面 Anti-de Sitter Gauss像 Legendrian奇点 |
Singularities of timelike Anti-de Sitter Gauss images of spacelike hypersurfaces in Anti-de Sitter n-space |
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| LIU HaiMing,MIAO JiaJing.Singularities of timelike Anti-de Sitter Gauss images of spacelike hypersurfaces in Anti-de Sitter n-space[J].Scientia Sinica Mathemation,2010,40(8):813-826. |
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| Authors: | LIU HaiMing MIAO JiaJing |
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| Institution: | LIU HaiMing , MIAO JiaJing |
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| Abstract: | We study spacelike hypersurfaces in Anti-de Sitter n-space as an application of singularity theory and we introduce the local differential geometry of spacelike hypersurfaces. We define the timelike Anti-de Sitter Gauss image and the Anti-de Sitter height function of spacelike hypersurfaces, which as a basic tool is used to investigate the geometric meanings of singularities of the timelike Anti-de Sitter Gauss image and the generic properties of spacelike hypersurfaces. At last, the AdS-Monge form is given. |
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| Keywords: | Anti-de Sitter n-space spacelike hypersurfaces AdS Gauss image Legendrian singularities |
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