Harmonic morphisms and shear-free ray congruences

Details Harmonic morphisms and shear-free ray congruences Harmonic morphisms and shear-free ray congruences

2003-06-27

arxiv.org/abs/math/0306390v1

Mathematics

Differential Geometry

38 pages, needs lms.sty, 3 ps figures. This is a revised and expanded version of dg-ga/9603005, and forms a supplement to the

Scientific paper

We describe the relationship between complex-valued harmonic morphisms from
Minkowski 4-space} and the shear-free ray congruences of mathematical physics.
Then we show how a horizontally conformal submersion on a domain of Euclidean
3-space gives the boundary values at infinity of a complex-valued harmonic
morphism on hyperbolic 4-space.

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