Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 214

The Dirac operator on Lorentzian spin manifolds and the Huygensproperty

H. Baum

We consider the Dirac operator $D$ of a Lorentzian spin manifold of even dimension $n geq 4$. We prove, that the square $D^2$ of the Dirac operator on plane wave manifolds and the shifted operator $D^2-K$ on Lorentzian space forms of constant sectional curvature $K$ are of Huygens type. Furthermore, we study the Huygens property for coupled Dirac operators on 4-dimensional Lorentzian spin manifolds.

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