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Holomorphic spinors and the Dirac equation

Klaus-Dieter Kirchberg
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Abstract

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 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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Klaus-Dieter Kirchberg. 1998-02-10. Holomorphic spinors and the Dirac equation. https://arxiv.org/abs/math/9802050

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