Harmonic morphisms in Hermitian geometry
We prove several results on holomorphic harmonic morphisms between Hermitian manifolds. In the non-compact case, we find conditions on holomorphic maps from domains in C-2 to C to retain the harmonicity when the metric is conformally changed. We conclude that there are no non-constant harmonic morphisms from S-4 minus a point to a Riemann surface. As for the compact case, we show that holomorphic
