The Dirac operator on Lorentzian spin manifolds and the Huygens property
The author investigates the Huygens property for the square \(D^2\) of the Dirac operator of a Lorentzian spin manifold of even dimension \(n\geq 4\). She proves that the operator \(D^2-K\) is of Huygens type if the underlying Lorentzian spin manifold has constant sectional curvature \(K\). Furthermore, \(D^2\) is of Huygens type on a plane wave manifold. Finally, the square of twisted Dirac operators on four-dimensional manifolds is considered. The author proves that the Huygens property of these operators implies that the coupling connection is flat and that the manifold belongs to one of three special classes of Lorentzian manifolds.
scientific article; zbMATH DE number 1051641
scientific article