| R1^m+1中拟迷向类空超曲面 |
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| 引用本文： | 姬秀,李同柱.R1^m+1中拟迷向类空超曲面[J].数学学报,2021,64(1):47-58. |
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| 作者姓名： | 姬秀 李同柱 |
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| 作者单位： | 北京理工大学数学与统计学院 北京 100081 |
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| 基金项目： | 国家自然科学基金资助项目（11571037） |
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| 摘 要： | 设f:M^m→R1^m+1是无脐点类空超曲面,则在Mm上可以定义四个基本的共形不变量:共形度量g,共形1-形式C,共形第二基本形式B,共形Blaschke张量A.如果存在光滑函数λ和常数μ,使得A+μB=Ag,则称M^m是拟迷向类空超曲面.本文不仅构造了拟迷向类空超曲面的例子,同时在相差R1^m+1的一个共形变换下,本文还完全分类了拟迷向类空超曲面.
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| 关 键 词： | 共形度量 共形第二基本形式 共形拟Blaschke张量 |
Para-isotropic Spacelike Hypersurfaces in R1m+1 |
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| Xiu JI,Tong Zhu LI.Para-isotropic Spacelike Hypersurfaces in R1m+1[J].Acta Mathematica Sinica,2021,64(1):47-58. |
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| Authors: | Xiu JI Tong Zhu LI |
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| Institution: | Department of Mathematics, Beijing Institute of Technology, Beijing 100081, P. R. China |
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| Abstract: | Let f:Mm → R1m+1 be an umbilic-free spacelike hypersurface. Four basic conformal invariants of Mm are the conformal metric g, the conformal 1-form C, the conformal second fundamental form B, and the conformal Blaschke tensor A. Mm is called the para-isotropic spacelike hypersurface, if A + μB=λg for some constant μ and smooth function λ. We not only constructed examples which are para-isotropic spacelike hypersurfaces but also classified completely all para-isotropic spacelike hypersurfaces under the conformal transformal group of R1m+1 in this paper. |
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| Keywords: | conformal metric conformal second fundamental form Conformal quasi Blaschke tensor |
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