Harmonic morphisms and shear-free ray congruences

2003/06/27 by P. Baird, J. C. Wood, Baird, P. +1
Mathematics · #53C43 (Primary) #58E20 (Secondary) #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53C43 #msc:58E20

paper · pdf · doi:10.48550/arxiv.math/0306390

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

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.

Related

• Harmonic morphisms, conformal foliations and shear-free ray congruences
• Shear-free ray congruences on curved space-times
• Harmonic morphisms from three-dimensional Euclidean and spherical space forms
• Hermitian structures and harmonic morphisms in higher dimensional Euclidean spaces
• Curvature conditions for complex-valued harmonic morphisms