GENERAL NON-EXISTENCE
 
         


Global
1. For m less than n, no non-constant harmonic morphisms from $M^m$ to $N^n$, 
   [P. 116: Fuglede 1978]


2. No non-constant harmonic morphisms from closed hyperbolic 3-manifolds 
   to a surface,
   [Cor. 3.12: Baird 1990]

3. No non-constant harmonic morphisms from $S^n+1$ to $S^n$ $(n\geq 4)$,
   [Cor. 4.8: Baird 1990]

4. No non-constant harmonic morphisms from compact manifolds of positive 
   {non-negative} Ricci curvature to manifolds of non-positive {negative} 
   scalar curvature,
   [Th. 2.5, (also Sec. 3): Mustafa to appear]


Local
1. No non-constant (local) harmonic morphisms from $Sol$ to $N^2$,
   [Th. 5.8(c): Baird-Wood 1992]



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