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.
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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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Batista, M., de Lima, H.F. & Santos, F.R.d. On the classification of MOTS in the de Sitter space. manuscripta math. 162, 159–169 (2020). https://doi.org/10.1007/s00229-019-01123-y
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DOI: https://doi.org/10.1007/s00229-019-01123-y