Biharmonic and harmonic homomorphisms between Riemannian three dimensional unimodular Lie groups

TL;DR

This paper classifies biharmonic and harmonic homomorphisms between three-dimensional unimodular Lie groups equipped with left invariant Riemannian metrics, providing a comprehensive understanding of such mappings.

Contribution

It offers a complete classification of biharmonic and harmonic homomorphisms for three-dimensional unimodular Lie groups with left invariant metrics, a previously unexplored area.

Findings

Classification of harmonic homomorphisms achieved

Biharmonic homomorphisms characterized explicitly

Results applicable to geometric analysis on Lie groups

Abstract

We classify biharmonic and harmonic homomorphisms $f:(G,g_1)\rightarrow(G,g_2)$ where $G$ is a connected and simply connected three-dimensional unimodular Lie group and $g_1$ and $g_2$ are left invariant Riemannian metrics.