Communications in Mathematical Physics

, Volume 169, Issue 2, pp 373–384

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

  • Andrei Moroianu
Article

DOI: 10.1007/BF02099477

Cite this article as:
Moroianu, A. Commun.Math. Phys. (1995) 169: 373. doi:10.1007/BF02099477

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.

Copyright information

© Springer-Verlag 1995

Authors and Affiliations

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