Classification of rotational surfaces in Euclidean space satisfying a linear relation between their principal curvatures

We classify all rotational surfaces in Euclidean space whose principal curvatures kappa(1) and kappa(2) satisfy the linear relation kappa 1=a kappa 2+b, where a and b are two constants. As a consequence of this classification, we find closed (embedded and not embedded) surfaces and periodic (embedded and not embedded) surfaces with a geometric behaviour similar to Delaunay surfaces. Finally, we give a variational characterization of the generating curves of these surfaces.