Hermitian structures and harmonic morphisms in higher dimensional Euclidean spaces

1994/10/13 by Baird, P., Wood, J. C.
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.dg-ga/9410005

Abstract

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 Rⁿ for each n>4 which do not arise from a Kähler structure; it is known that such examples do not exist for n ≤ 4.

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