  In this paper we generalize a classical result of Bour concerning helicoidal
surfaces in the three-dimensional Euclidean space R^3 to the case of helicoidal
surfaces in the Bianchi-Cartan-Vranceanu (BCV) spaces, i.e. in the Riemannian
3-manifolds whose metrics have groups of isometries of dimension $4$ or $6$,
except the hyperbolic one. In particular, we prove that in a BCV-space there
exists a two-parameter family of helicoidal surfaces isometric to a given
helicoidal surface; then, by making use of this two-parameter representation,
we characterize helicoidal surfaces which have constant mean curvature,
including the minimal ones.
