Biharmonic homomorphisms between Riemannian Lie groups

TL;DR

This paper investigates harmonic and biharmonic homomorphisms between Riemannian Lie groups, revealing their potential for constructing examples and posing interesting mathematical challenges in the theory of Riemannian Lie groups.

Contribution

It provides a detailed study of biharmonic homomorphisms between Riemannian Lie groups and explores their applications and theoretical implications.

Findings

Biharmonic maps can be used to construct examples of Riemannian Lie group homomorphisms.

The study of biharmonic homomorphisms leads to new mathematical problems in Riemannian Lie group theory.

Insights into the structure of harmonic and biharmonic maps between Lie groups.

Abstract

A Lie group $G$ endowed with a left invariant Riemannian metric $g$ is called Riemannian Lie group. Harmonic and biharmonic maps between Riemannian manifolds is an important area of investigation. In this paper, we study different aspects of harmonic and biharmonic homomorphisms between Riemannian Lie groups. We show that this class of biharmonic maps can be used at the first level to build examples but, as we will see through this paper, its study will lead to some interesting mathematical problems in the theory of Riemannian Lie groups.