Linear \infty-Harmonic maps between Rienmannian manifolds

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