Holomorphic spinors and the Dirac equation

Mathematics – Differential Geometry

Scientific paper

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Latex2.09, 14 pages

Scientific paper

A closed spin K\"ahler 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 K\"ahler-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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