Transitivity domains of groups of similarities (Q1114163)

In this nicely written paper, the author shows by means of elementary and well-known results from Euclidean geometry that if a group G of similarities acts transitively on an open subset X of a real affine n- space then, essentially, X is \(A^ n\) or a half-space or a complement of a lower dimensional affine subspace. He also points out applications of his result to Riemannian structures and to convex geometry.