Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 290

Holomorphic spinors and the Dirac equation

K.-D. Kirchberg

A closed spin Kaehler manifold of positive scalar curvature with smallest possible first eigenvalue of the Dirac operator is characterized by holomorphic spinors. It is shown that on any spin Kaehler-Einstein manifold each holomorphic spinor is a finite sum of eigenspinors of the square of the Dirac operator. Vanishing theorems for holomorphic spinors are proved.

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