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On the classification of MOTS in the de Sitter space

  • Márcio Batista
  • Henrique F. de LimaEmail author
  • Fábio R. dos Santos
Article
  • 42 Downloads

Abstract

In this paper, we deal with marginally outer trapped surfaces (MOTS) immersed in the de Sitter space \(\mathbb {S}_1^{n+2}\). In this setting we are able to obtain a Simons formula for the null second fundamental form and under some appropriate constraints on the MOTS, we apply a weak maximum principle in order to guarantee that it must be either a totally geodesic submanifold or isometric to an open piece of an isoparametric submanifold with two distinct principal curvatures one of which is simple. In this last case, supposing that the initial data where the MOTS lying is a totally umbilical spacelike hypersurface of \(\mathbb {S}_1^{n+2}\), we conclude that it must be either isometric to a circular cylinder, a hyperbolic cylinder or a Clifford torus.

Mathematics Subject Classification

Primary 53C42 53C50 Secondary 53A10 53C20 

Notes

Acknowledgements

The authors would like to thank the referee for his/her comments and suggestions which enabled them to improve this work. The first author is partially supported by CNPq, Brazil, Grant 456755/2014-4 and FAPEAL. The second author is partially supported by CNPq, Brazil, Grant 303977/2015-9. The third author is partially supported by CNPq, Brazil, Grant 431976/2018-0.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.CPMAT-IMUniversidade Federal de AlagoasMaceióBrazil
  2. 2.Departamento de MatemáticaUniversidade Federal de Campina GrandeCampina GrandeBrazil

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