Holomorphic Spinors and the Dirac Equation

A closed spin Kähler 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 Kähler-Einstein manifold each holomor-phic spinor is a finite sum of eigenspinors of the square of the Dirac operator. Vanishing theorems for holomorphic spinors are… CONTINUE READING