GENERAL  CONSTRUCTIONS
of harmonic morphisms $(M^m,g)\to (N^n,h)$ between Riemannian manifolds


Basics
1. the composition of harmonic morphisms.



Holomorphic
1. conformal maps between open subsets of the plane
   [Gehring-Haahti 1960]

2. holomorphic functions $U\subset C^n\to C$,
   [p.114: Fuglede 1978]

3. holomorphic maps $(M,g,J)\to N^2$ from Kähler manifolds to Riemann surfaces,
   [Baird-Eells 1981]

4. certain holomorphic maps $(M,g,J)\to (N,h,J_N)$ between almost Hermitian
   manifolds, [Gudmundsson-Wood 1996]


Submersions  with  minimal  fibres
1. Riemannian submersions with minimal fibres,
   [p.140: Fuglede 1978]

2. n=2: horizontally conformal submersions with minimal fibres,
   [Baird-Eells 1981]

3. n>2: horizontally homothetic, conformal submersions with minimal
   fibres, [Baird-Eells 1981].

4. projections from warped products $M\times_f N\to N$,
   [Wood 1986]


Lie  groups
1. the multiplication of Lie groups $G\times G\to G$,
   [p.140: Fuglede 1978]

2. the projection maps $G\to G/K$ for the irreducible symmetric spaces,
   [thesis ch.6: Gudmundsson 1992]


Isoparametric  foliations
1. totally umbilic isoparametric families of codimension 1,
   [Baird 1983]

2. totally umbilic isoparametric families of higher codimension,
   [Gudmundsson 1992]


Reduction  via  invariance
1. reduction through $R^4-{point}\to S^3$ via $R^+$-invariance,
   [sec. 6: Baird 1987]

2. reduction through submersive harmonic morphisms $\pi:\hat M\to M$
   through invariance, [sec. 1: Gudmundsson 1994]

Branched  coverings
1. harmonic morphisms as branched coverings over surfaces,
   [Gudmundsson-Wood 1993]

Complete  lifts
1. the complete lifts of harmonic morphisms satisfying two additional
   conditions, [Prop. 2.7: Ou 1995]

2. the complete lifts of quadradic harmonic morphisms,
   [Thm. 3.3: Ou 1995]



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