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Spacelike Möbius Hypersurfaces in Four Dimensional Lorentzian Space Form

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Abstract

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.

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Acknowledgements

We thank the referees for their valuable comments.

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Authors and Affiliations

  1. College of Mathematics and Informatics, Fujian Normal University, Fuzhou, 350117, P. R. China

    Yan Bin Lin & Chang Ping Wang

  2. School of Mathematical Sciences, Xiamen University, Xiamen, 361005, P. R. China

    Ying Lü

Authors
  1. Yan Bin Lin
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  2. Ying Lü
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  3. Chang Ping Wang
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Corresponding authors

Correspondence to Yan Bin Lin, Ying Lü or Chang Ping Wang.

Additional information

The second author is supported by NSFC (Grant Nos. 11571287 and 11671330), the third is supported by NSFC (Grant Nos. 11331002 and 11471021)

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Lin, Y.B., Lü, Y. & Wang, C.P. Spacelike Möbius Hypersurfaces in Four Dimensional Lorentzian Space Form. Acta. Math. Sin.-English Ser. 35, 519–536 (2019). https://doi.org/10.1007/s10114-019-8042-0

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  • DOI: https://doi.org/10.1007/s10114-019-8042-0

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