Spacelike Möbius Hypersurfaces in Four Dimensional Lorentzian Space Form
Spacelike Möbius Hypersurfaces in Four Dimensional Lorentzian Space Form
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DOI：
10.1007/s10114-019-8042-0
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发表时间：
2019-03
期刊：
影响因子：
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通讯作者：
Y. Lin;Ying Lü;Changping Wang
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文献类型：
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作者：
Y. Lin;Ying Lü;Changping Wang
本文首先建立了四维Lorentz空间形式中任意无脐类空超曲面的Möbius几何的另一基本理论，证明了这类超曲面可以完全由函数W和切框架{Ei}组成的系统确定.然后给出了四维洛伦兹空间形式中类空Möbius齐次超曲面的一个完全分类。它们要么是莫比乌斯等价于类空的杜宾超曲面，要么是由对数曲线和双曲对数螺线构造的某些圆柱。它们中的一些具有非零莫比乌斯形式的平行para-Blaschke张量。
In this paper, we first set up an alternative fundamental theory of Möbius geometry for any umbilic-free spacelike hypersurfaces in four dimensional Lorentzian space form, and prove the hypersurfaces can be determined completely by a system consisting of a function W and a tangent frame {Ei}. Then we give a complete classification for spacelike Möbius homogeneous hypersurfaces in four dimensional Lorentzian space form. They are either Möbius equivalent to spacelike Dupin hypersurfaces or to some cylinders constructed from logarithmic curves and hyperbolic logarithmic spirals. Some of them have parallel para-Blaschke tensors with non-vanishing Möbius form.