Journal of geometry and physics vol:40 issue:1 pages:47-55
The complex vectorial formalism on a general space-time (M, g) was constructed by Cahen, Debever and Defrise. This formalism is based on the local isomorphism I : L(4) --> SO3(C), where L(4) is the four-dimensional Lorentz group acting on the tangent spaces TpM and SO3 (C) is the three-dimensional complex rotation group. In this framework, the congruence of Debever plays a distinguished role. Its properties determine the general space-time M, in terms of Petrov's classification.