
Journal for Geometry and Graphics 14 (2010), No. 2, 181186 Copyright Heldermann Verlag 2010 Surfaces of Revolution Satisfying Δ^{III}x = Ax Stylianos Stamatakis Dept. of Mathematics, Aristotle University, 54124 Thessaloniki, Greece stamata@math.auth.gr Hassan AlZoubi Dept. of Mathematics, Aristotle University, 54124 Thessaloniki, Greece We consider surfaces of revolution in the threedimensional Euclidean space which are of coordinate finite type with respect to the third fundamental form III, i.e., their position vector x satisfies the relation Δ^{III}x = Ax, where A is a square matrix of order 3. We show that a surface of revolution satisfying the preceding relation is a catenoid or part of a sphere. Keywords: Surfaces in the Euclidean space, surfaces of coordinate finite type, Beltrami operator. MSC: 53A05; 47A75 [ Fulltextpdf (104 KB)] for subscribers only. 