The twistor equation on Riemannian manifolds

Abstract

It is shown that a twistor spinor on a Riemannian manifold defines a conformal deformation to an Einstein manifold. Twistor spinors on 4-manifolds are considered. A characterization of the hyperbolic space is given. Moreover the solutions of the twistor equation on warped products M n × M n× R , where M n is an Einstein manifold, are described.