Biconformal changes of metric and pseudo-harmonic morphisms

TL;DR

This paper investigates how biconformal metric changes preserve the properties of pseudo-harmonic morphisms and explores the special case of pseudo-horizontally homothetic harmonic morphisms.

Contribution

It demonstrates that certain geometric properties of pseudo-harmonic morphisms are invariant under biconformal metric transformations.

Findings

Biconformal changes preserve harmonicity of pseudo-harmonic morphisms.

The almost complex structure on the distribution remains compatible after the change.

Special case of pseudo-horizontally homothetic harmonic morphisms is analyzed.

Abstract

Pseudo-harmonic morphisms give rise on the domain space to a distribution which admits an almost complex structure compatible with the given Riemannian metric. We shall show that this property, together with the harmonicity, are preserved by a biconformal change of the domain metric. The special case of the pseudo-horizontally homothetic harmonic morphisms is also treated.