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arXiv · 0910.1036

Harmonic morphisms and bicomplex manifolds

Paul Baird·John C. Wood
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Abstract

We use functions of a bicomplex variable to unify the existing constructions of harmonic morphisms from a 3-dimensional Euclidean or pseudo-Euclidean space to a Riemannian or Lorentzian surface. This is done by using the notion of complex-harmonic morphism between complex-Riemannian manifolds and showing how these are given by bicomplex-holomorphic functions when the codomain is one-bicomplex dimensional. By taking real slices, we recover well-known compactifications for the three possible real cases. On the way, we discuss some interesting conformal compactifications of complex-Riemannian manifolds by interpreting them as bicomplex manifolds.

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Paul Baird, John C. Wood. 2010-03-11. Harmonic morphisms and bicomplex manifolds. https://arxiv.org/abs/0910.1036

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