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R1m+1中拟迷向类空超曲面
Para-isotropic Spacelike Hypersurfaces in R1m+1
设f ：Mm → R1m+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=λg，则称Mm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R1m+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.
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.
共形度量 / 共形第二基本形式 / 共形拟Blaschke张量 {{custom_keyword}} /
conformal metric / conformal second fundamental form / Conformal quasi Blaschke tensor {{custom_keyword}} /
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国家自然科学基金资助项目（11571037）
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