Abstract. We simplify and generalize Cartan's results on Cauchy-Riemann spaces admitting continuous groups of automorphisms. We describe all such spaces in terms of local coordinates. Cauchy-Riemann spaces [ 1] appear in physics in the context of algebraically special solutions of the Einstein equations and null solutions of the Maxwell (or Yang-Mills) equations [2-4]. In both cases, spacetime admits a shearfree geodesic null congruence. This property is equivalent to the following condition on the metric tensor [5
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