Linear \infty-Harmonic maps between Rienmannian manifolds

TL;DR

This paper classifies linear -harmonic maps and endomorphisms between specific geometric spaces, revealing structural properties and automorphism subgroups within these mappings.

Contribution

It provides a complete classification of linear -harmonic maps between Euclidean, Heisenberg, Nil, and Sol spaces, and identifies a subgroup of automorphisms in Sol space.

Findings

Complete classification of linear -harmonic maps between Euclidean and Heisenberg spaces

Classification of -harmonic linear endomorphisms of Sol space

Existence of a subgroup of -harmonic linear automorphisms in Sol space

Abstract

In this paper, we give complete classifications of linear $\infty$-harmonic maps between Euclidean and Heisenberg spaces, between Nil and Sol spaces. We also classify all $\infty$-harmonic linear endomorphisms of Sol space and show that there is a subgroup of $\infty$-harmonic linear automorphisms in the group of linear automorphisms of Sol space.