Journal for Geometry and Graphics 14 (2010), No. 2, 181--186
Copyright Heldermann Verlag 2010
Surfaces of Revolution Satisfying ΔIIIx = Ax
Stylianos Stamatakis
Dept. of Mathematics, Aristotle University, 54124 Thessaloniki, Greece
stamata@math.auth.gr
Hassan Al-Zoubi
Dept. of Mathematics, Aristotle University, 54124 Thessaloniki, Greece
We consider surfaces of revolution in the three-dimensional 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 ΔIIIx = 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
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