The Dirac operator on Lorentzian spin manifolds and the Huygens property

We consider the Dirac operator D of a Lorentzian spin manifold of even dimension n ≥ 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 t...

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Bibliographic Details
Published in:Journal of geometry and physics 1997-08, Vol.23 (1), p.42-64
Main Author: Baum, Helga
Format: Article
Language:English
Subjects:
Dirac operator
Huygens principle
Lorentzian spin manifolds
Spinors and twistors
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Summary:We consider the Dirac operator D of a Lorentzian spin manifold of even dimension n ≥ 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 four-dimensional Lorentzian spin manifolds.
ISSN:0393-0440
1879-1662
DOI:10.1016/S0393-0440(96)00045-9