Harmonic morphisms and shear-free ray congruences
Differential Geometry
2007-05-23 v1
Abstract
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.
Cite
@article{arxiv.math/0306390,
title = {Harmonic morphisms and shear-free ray congruences},
author = {P. Baird and J. C. Wood},
journal= {arXiv preprint arXiv:math/0306390},
year = {2007}
}
Comments
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 authors' book `Harmonic morphisms between Riemannian manifolds', see http://www.amsta.leeds.ac.uk/Pure/staff/wood/BWBook/BWBook.html