Complex contact structures and the first eigenvalue of the Dirac operator on Kähler manifolds (Q1895261)

Due to an estimate by K. D. Kirchberg every eigenvalue \(\lambda\) of the Dirac operator on a closed spin Kähler manifold of odd complex dimension \(m\) satisfies \(\lambda^2\geq (m+ 1)R_0/4m\) where \(R_0\) is the minimum of the scalar curvature. In the equality case the corresponding eigenspinors are Kählerian Killing spinors and the manifold is Einstein. The authors investigate the relation between Kählerian Killing spinors and complex contact structures. Independently \textit{A. Moroianu} [Commun. Math. Phys. 169, No. 2, 373-384 (1995; Zbl 0832.53054)] gave a complete description of manifolds with Kählerian Killing spinors of odd complex dimension.