Harmonic morphisms and bicomplex manifolds

Who: John Wood (Leeds)
When: Monday, January 11, 2010 at 14:15
Where: The CP³ meeting room

Harmonic morphisms are map which preserves Laplace’s equation; they can be characterized as harmonic maps which enjoy a partial conformality condition. We use functions of a bicomplex variable to give unified constructions of harmonic morphisms for different signatures. This uses the notion of complex-harmonic morphism between complex-Riemannian manifolds; we show how these are given by bicomplex-holomorphic functions on a bicomplex manifold when the codomain is one-bicomplex dimensional. On the way, we discuss some interesting conformal compactifications of complex-Riemannian manifolds by interpreting them as bicomplex manifolds such as the bicomplex quadric.