EIGENVALUES OF THE DIRAC OPERATOR ON COMPACT KAHLER-MANIFOLDS

Kahlerian twistor operators are introduced to get lower bounds for the eigenvalues of the Dirac operator on compact spin Kahler manifolds. In odd complex dimensions, manifolds with the smallest eigenvalues are characterized by an over determined system of differential equations similar to the Riemannian case. In these dimensions, we show the existence of a unique natural Kahlerian twistor operator. It is also proved that, on a Kahler manifold with nonzero scalar curvature, the space of Riemannian twistor-spinors is trivial.