An indecomposable Riemannian symmetric space which admits nontrivial twistor spinors has constant sectional curvature. Furthermore, each homogeneous Riemannian manifold with parallel spinors is at. In the present paper we solve the twistor equation on all indecomposable Lorentzian symmetric spaces explicitly. In particular, we show that there are-in contrast to the Riemannian case-indecom-posab...

We investigate connections between pairs of Riemannian metrics whose sum is a (tensor) product of a covector field with itself. As a special result is constructed one-to-one mapping between the classes of Euclidean and Lorentzian metrics. The existence of Lorentzian metrics on a differentiable manifold is discussed. We point the possibility that any physical theory based on Lorentzian metric(s)...

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 4-dimensional Lorentzian spin manifolds.