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On the complete spacelike hypersurfaces immersed with two distinct principal curvatures in a locally symmetric Lorentz space

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Abstract

Our purpose in this paper is to study the geometry of complete linear Weingarten spacelike hypersurfaces immersed with two distinct principal curvatures in a locally symmetric Lorentz space, which is supposed to obey standard curvature constrains. In this setting, we apply some appropriated generalized maximum principles to a suitable Cheng-Yau modified operator in order to guarantee that such a spacelike hypersurface must be isometric to an isoparametric hypersurface of the ambient space.

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Acknowledgments

The first author is partially supported by CNPq, Brazil, grant 300769/2012-1. The second author is partially supported by CAPES, Brazil. The third author is partially supported by PRONEX/CNPq/FAPEAM, Brazil, Grant 716.UNI52.1769.03062009. The authors would like to thank the referee for giving valuable suggestions which improved the paper.

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Correspondence to Henrique F. de Lima.

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de Lima, H.F., dos Santos, F.R., Gomes, J.N. et al. On the complete spacelike hypersurfaces immersed with two distinct principal curvatures in a locally symmetric Lorentz space. Collect. Math. 67, 379–397 (2016). https://doi.org/10.1007/s13348-015-0145-z

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