La première valeur propre de l’opérateur de Dirac sur les variétés kählériennes compactes
K. D. Kirchberg gave a lower bound for the first eigenvalue of the Dirac operator on a spin compact K"ahler manifold $M$ of odd complex dimension with positive scalar curvature. We prove that manifolds satisfying the limiting case are twistor space of quaternionic K"ahler manifold with positive scalar curvature.
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