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Dirac Operators on Time Flat Submanifolds with Applications

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Abstract

In this paper, we study Dirac-type operators on time flat submanifolds in spacetimes satisfying the Einstein equations with non positive cosmological constant. We apply our results to obtain global rigidity results for n-dimensional time flat submanifolds in the Minkowski spacetime as well as in the anti-de Sitter spacetime.

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Authors and Affiliations

  1. Institut Élie Cartan, Université de Lorraine, B.P. 239, 54506, Vandœuvre-Lès-Nancy Cedex, France

    Oussama Hijazi

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

    Sebastián Montiel

  3. Laboratoire de Mathématiques R. Salem UMR 6085 CNRS, Université de Rouen, Avenue de l’Université, Technopôle du Madrillet, B.P. 12, 76801, Saint-Étienne-du-Rouvray, France

    Simon Raulot

Authors
  1. Oussama Hijazi
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  2. Sebastián Montiel
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  3. Simon Raulot
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Corresponding author

Correspondence to Oussama Hijazi.

Additional information

Communicated by P. T. Chruściel

Sebastián Montiel was partially supported by a Spanish MEC-FEDER Grant No. MTM2011-22547.

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Hijazi, O., Montiel, S. & Raulot, S. Dirac Operators on Time Flat Submanifolds with Applications. Commun. Math. Phys. 351, 1177–1194 (2017). https://doi.org/10.1007/s00220-017-2837-6

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  • DOI: https://doi.org/10.1007/s00220-017-2837-6

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