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Integral formulas for compact spaceliken-submanifolds in de Sitter spaces applications to the parallel mean curvature vector case

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Abstract

We introduce a new method to study compact spaceliken-submanifolds in de Sitter spacesS n+q q by means of certain integral formulas which have a very clear geometric meaning. As a first application of them we obtain a Bernstein type result for complete maximal submanifolds inS n+q q . As for surfaces, we also get a uniqueness result for compact spacelike surfaces inS 2+q q with parallel mean curvature vector field.

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad de Murcia, Campus de Espinardo, 30100, Espinardo, Murcia, Spain

    Luis J. Alías

  2. Departamento de Geometría y Topología, Universidad de Granada, Campus de Fuentenueva, 18071, Granada, Spain

    Alfonso Romero

Authors
  1. Luis J. Alías
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  2. Alfonso Romero
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Partially supported by a DGICYT Grant No. PB91-0705-C02-02

Partially supported by a DGICYT Grant No. PB91-0731

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Alías, L.J., Romero, A. Integral formulas for compact spaceliken-submanifolds in de Sitter spaces applications to the parallel mean curvature vector case. Manuscripta Math 87, 405–416 (1995). https://doi.org/10.1007/BF02570483

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  • DOI: https://doi.org/10.1007/BF02570483

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