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On Non-degenerate Null Normal Sections of Codimension Two Spacelike Surfaces

  • Daniel de la Fuente
  • Francisco J. Palomo
  • Alfonso RomeroEmail author
Article
  • 64 Downloads

Abstract

In this paper, we develop a formula for spacelike surfaces in a four-dimensional Lorentzian space form which involves its mean curvature vector field, the Gauss curvature of the induced metric and the Gauss curvature of the second fundamental form associated to a non-degenerate null normal section. By means of this formula, we establish several sufficient conditions for a compact spacelike surface in a four-dimensional Lorentzian space form which has a null umbilical normal direction. As another application, we give a new proof of Liebmann rigidity theorems in Euclidean, hemispherical, hyperbolic spaces and in the De Sitter spacetime.

Keywords

Spacelike surface Gauss curvature Liebmann theorem Lorentzian space forms 

Mathematics Subject Classification

53C24 53C50 53C42 

Notes

Acknowledgements

We would like to thank the Referees of the paper, specially to Referee \(\#2\) for his/her careful reading and suggestions to improve the previous version of the manuscript.

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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2017

Authors and Affiliations

  • Daniel de la Fuente
    • 1
  • Francisco J. Palomo
    • 2
  • Alfonso Romero
    • 1
    Email author
  1. 1.Departamento de Geometría y TopologíaUniversidad de GranadaGranadaSpain
  2. 2.Departamento de Matemática AplicadaUniversidad de MálagaMálagaSpain

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