2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67365In this paper we discuss the twistor equation in Lorentzian spin geometry. In particular, we explain the local conformal structure of Lorentzian manifolds, which admit twistor spinors inducing lightlike Dirac currents. Furthermore, we derive all local geometries with singularity free twistor spinors that occur up to dimension 7.20 pagesDifferential Geometry53C15;53C50text