Helix surfaces in Euclidean spaces

We study helix surfaces with parallel mean curvature vector in Euclidean space from a local point of view. Our main result says that they are either part of a cylinder of revolution or a plane. One way to prove this is with the generalization we found about the Laplacian of a support function of a hypersurface. This allows us to study the constant mean curvature surfaces in space forms which have constant angle with respect to a closed and conformal vector field. The result we find says that these surfaces are totally umbilic.