Communications in Mathematical Physics

, Volume 104, Issue 1, pp 151–162 | Cite as

A conformal lower bound for the smallest eigenvalue of the Dirac operator and killing spinors

  • Oussama Hijazi


On a Riemannian spin manifold, we give a lower bound for the square of the eigenvalues of the Dirac operator by the smallest eigenvalue of the conformal Laplacian (the Yamabe operator). We prove, in the limiting case, that the eigenspinor field is a killing spinor, i.e., parallel with respect to a natural connection. In particular, if the scalar curvature is positive, the eigenspinor field is annihilated by harmonic forms and the metric is Einstein.


Neural Network Manifold Statistical Physic Complex System Nonlinear Dynamics 
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Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • Oussama Hijazi
    • 1
  1. 1.Max-Planck-Institut für MathematikBonn 3Germany

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