2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/141412In 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.22 PagesDifferential GeometryAnalysis of PDEs58E20, 53C12text