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On the Angle of Complete Hypersurfaces in Semi-Riemannian Product Spaces

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Abstract

The purpose of this article is to study the uniqueness of complete hypersurfaces satisfying some pinching curvature condition. Here, we use the generalized maximum principle of Omori–Yau to obtain uniqueness results for complete spacelike hypersurfaces immersed in a Lorentzian product space. In addition, we obtain the analogue results for complete hypersurfaces immersed in a Riemannian product space.

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Acknowledgements

The authors would like to thank E. Ribeiro Jr. for helpful conversations that benefited the presentation of this paper. The first author is partially supported by CNPq, Brazil, Grant 302738/2014-2.

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Author notes

  1. Halyson Baltazar

    Present address: Departamento de Matemática, Universidade Federal do Ceará - UFC, Campus do Pici, Fortaleza, CE, 60455-760, Brazil

Authors and Affiliations

  1. Departamento de Matemática, Universidade Federal do Piauí, Teresina, Piauí, 64049-550, Brazil

    Cícero Aquino & Halyson Baltazar

Authors
  1. Cícero Aquino
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  2. Halyson Baltazar
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Corresponding author

Correspondence to Cícero Aquino.

Additional information

H. Baltazar was partially supported by CNPq/Brazil. C. Aquino was partially supported by CNPq/Brazil, Grant 302738/2014-2.

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Aquino, C., Baltazar, H. On the Angle of Complete Hypersurfaces in Semi-Riemannian Product Spaces. Bull Braz Math Soc, New Series 48, 697–715 (2017). https://doi.org/10.1007/s00574-017-0041-0

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  • DOI: https://doi.org/10.1007/s00574-017-0041-0

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