HARMONIC MORPHISMS, CONFORMAL FOLIATIONS AND SHEAR-FREE RAY CONGRUENCES

A shear-free ray congruence is a foliation by null lines (light rays) of an open subset of Minkowski space satisfying a certain conformality condition. We show that (i) any real-analytic complex-valued harmonic morphism without critical points defined on an open subset of Minkows ki space is conformally equivalent to the direction vector held of a s hear-free ray congruence, (ii) any (real-analytic) complex-valued hori zontally conformal submersion on an open subset of R-3 is locally the boundary values at infinity of a harmonic morphism on an open subset o f hyperbolic space. This provides a construction of families of minima l surfaces in hyperbolic 4-space with given boundaries at infinity.