The aim of this paper is to study some examples of exponentially harmonic
maps. We study such maps firstly on flat euclidean and Minkowski spaces and
secondly on Friedmann-Lema\^ itre universes. We also consider some new models
of exponentially harmonic maps which are coupled with gravity which happen to
be based on a generalization of the lagrangian for bosonic strings coupled with
dilatonic field.Comment: 16 pages, 5 figure