Proper p-harmonic functions and harmonic morphisms on the classical non-compact semi-Riemannian Lie groups

TL;DR

This paper constructs explicit complex-valued p-harmonic functions and harmonic morphisms on non-compact classical Lie groups using eigenfamilies, advancing understanding of semi-Riemannian geometry on these groups.

Contribution

It introduces a method to explicitly generate p-harmonic functions and harmonic morphisms on non-compact classical Lie groups with semi-Riemannian metrics.

Findings

Explicit complex-valued p-harmonic functions constructed

Explicit harmonic morphisms constructed

Method applicable to non-compact classical Lie groups

Abstract

We apply the method of eigenfamilies to construct new explicit complex-valued p-harmonic functions on the non-compact classical Lie groups, equipped with their natural semi-Riemannian metrics. We then employ this same approach to manufacture explicit complex-valued harmonic morphisms on these groups.