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

Abstract

K.D. Kirchberg [Ki1] gave a lower bound for the first eigenvalue of the Dirac operator on a spin compact Kahler 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 Kahler 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.