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We classify all rotational surfaces in Euclidean space whose principalcurvatures $\kappa_1$ and $\kappa_2$ satisfy the linear relation$\kappa_1=a\kappa_2+b$, where $a$ and $b$ are two constants. We give avariational characterization of these surfaces in terms of its generatingcurve. As a consequence of our classification, we find closed (embedded and notembedded) surfaces and periodic (embedded and not embedded) surfaces with ageometric behaviour similar to Delaunay surfaces.

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