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Spacelike Möbius Hypersurfaces in Four Dimensional Lorentzian Space Form

  • Yan Bin LinEmail author
  • Ying Lü
  • Chang Ping Wang
Article
  • 6 Downloads

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.

Keywords

Möbius form Möbius metric para-Blaschke tensor Möbius homogeneous hypersurface hyperbolic logarithmic spiral Dupin hypersurface 

MR(2010) Subject Classification

53A30 53B25 

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Notes

Acknowledgements

We thank the referees for their valuable comments.

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Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science (CAS), Chinese Mathematical Society (CAS) and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.College of Mathematics and InformaticsFujian Normal UniversityFuzhouP. R. China
  2. 2.School of Mathematical SciencesXiamen UniversityXiamenP. R. China

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