GENERAL  INFORMATION

Harmonic morphisms are maps (M^m,g) --> (N^n,h) between Riemannian
manifolds which pull back locally defined real-valued harmonic functions
on (N^n,h) to harmonic functions on (M^m,g).  They form a special class
of harmonic maps, namely those which are (weakly) horizontally conformal.
This means that harmonic morphisms are solutions to an over-determined
system of partial differential equations.


The case when the manifold N is a surface, i.e. of dimension 2, is of
particular interest. Then harmonic morphisms (M,g) --> (N^2,h) have
many nice geometric properties.  Every regular fibre of such a map
is a minimal submanifold of (M^m,g) of codimension 2.  This means
that harmonic morphisms are useful tools for the construction of
such submanifolds.  Interesting examples are holomorphic maps
from Kähler manifolds to Riemann surfaces.