A New Approach to Rotational Weingarten Surfaces

Weingarten surfaces are those whose principal curvatures satisfy a functional relation, set of solutions is called the curvature diagram or W-diagram surface. Making use notion geometric linear momentum plane curve, we propose new approach to study rotational in Euclidean 3-space. Our contribution consists reducing any type condition on surface first-order differential equation generatrix curve. In this line, provide two classification results involving cubic and an hyperbola characterizing, respectively, non-degenerated quadric revolution elasticoids, defined as generated by rotation Euler elastic curves around their directrix line. As another application our approach, deal with problem prescribing mean Gauss terms arbitrary continuous functions depending distance from axis revolution. consequence, simple proofs some classical concerning surfaces, such Euler’s theorem about minimal ones, Delaunay’s constant Darboux’s ones.