Proper biharmonic maps and $(2,1)$-harmonic morphisms from some wild geometries

TL;DR

This paper constructs new complex-valued proper biharmonic maps and (2,1)-harmonic morphisms on Riemannian manifolds with complex geometries, solving related nonlinear PDE systems.

Contribution

It introduces novel proper biharmonic maps and (2,1)-harmonic morphisms tailored to complex geometries, expanding the class of known solutions.

Findings

New proper biharmonic maps constructed

(2,1)-harmonic morphisms developed

Solutions depend on manifold geometric data

Abstract

In this work we construct a variety of new complex-valued proper biharmonic maps and (2,1)-harmonic morphisms on Riemannian manifolds with non-trivial geometry. These are solutions to a non-linear system of partial differential equations depending on the geometric data of the manifolds involved.