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The Dirac–Witten operator on pseudo-Riemannian manifolds

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We study the Dirac–Witten operator for spacelike spin submanifolds in pseudo-Riemannian manifolds. When the normal bundles are spin and odd-dimensional, we derive new eigenvalue lower bounds. We also prove the generalized positive mass theorem using this operator.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, Poeple’s Republic of China

    Daguang Chen

  2. Institut Élie Cartan Université Henri Poincaré, Nancy 1, B.P. 239, 54506, Vandoeuvre-Lès-Nancy Cedex, France

    Oussama Hijazi

  3. Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, Poeple’s Republic of China

    Xiao Zhang

Authors
  1. Daguang Chen
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  2. Oussama Hijazi
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  3. Xiao Zhang
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Correspondence to Oussama Hijazi.

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Chen, D., Hijazi, O. & Zhang, X. The Dirac–Witten operator on pseudo-Riemannian manifolds. Math. Z. 271, 357–372 (2012). https://doi.org/10.1007/s00209-011-0867-x

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  • DOI: https://doi.org/10.1007/s00209-011-0867-x

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