Communications in Mathematical Physics

, Volume 169, Issue 2, pp 373–384 | Cite as

La première valeur propre de l'opérateur de Dirac sur les variétés kählériennes compactes

  • Andrei Moroianu
Article

Abstract

K.D. Kirchberg [Ki1] gave a lower bound for the first eigenvalue of the Dirac operator on a spin compact Kähler manifoldM of odd complex dimension with positive scalar curvature. We prove that manifolds of real dimension 8l+6 satisfying the limiting case are twistor space (cf. [Sa]) of quaternionic Kähler manifold with positive scalar curvature and that the only manifold of real dimension 8l+2 satisfying the limiting case is the complex projective spaceCP4l+1.

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Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Andrei Moroianu
    • 1
  1. 1.Centre de MathématiquesEcole PolytechniquePalaiseauFrance

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