Complex-valued (p,q)-harmonic morphisms from Riemannian manifolds

TL;DR

This paper introduces (p,q)-harmonic morphisms between Riemannian manifolds, unifying previous theories, and provides new characterizations and examples for complex-valued cases.

Contribution

It defines the concept of (p,q)-harmonic morphisms and offers new characterizations and non-trivial examples for complex-valued maps.

Findings

Unified several theories of harmonic morphisms

Characterized complex-valued (p,q)-harmonic morphisms

Constructed new non-trivial examples

Abstract

We introduce the natural notion of (p,q)-harmonic morphisms between Riemannian manifolds. This unifies several theories that have been studied during the last decades. We then study the special case when the maps involved are complex-valued. For these we find a characterisation and provide new non-trivial examples in important cases.