Hermitian structures and harmonic morphisms in higher dimensional Euclidean spaces

Mathematics – Differential Geometry

Scientific paper

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34 pages, preprint, University of Leeds, 94-13

Scientific paper

We construct new complex-valued harmonic morphisms from Euclidean spaces from
functions which are holomorphic with respect to Hermitian structures. In
particular, we give the first global examples of complex-valued harmonic
morphisms from ${\bf R}^n$ for each $n>4$ which do not arise from a K\"ahler
structure; it is known that such examples do not exist for $n \leq 4$.

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