Geodesic
Surfaces of Revolution Satisfying ΔIIIx = Ax
Journal for geometry and graphics, Tome 14 (2010) no. 2, pp. 181-186.

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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.
Classification : 53A05, 47A75
Mots-clés : Surfaces in the Euclidean space, surfaces of coordinate finite type, Beltrami operator 
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     author = {S. Stamatakis and H. Al-Zoubi },
     title = {Surfaces of {Revolution} {Satisfying} {\ensuremath{\Delta}\protect\textsuperscript{III}x} = {Ax}},
     journal = {Journal for geometry and graphics},
     pages = {181--186},
     publisher = {mathdoc},
     volume = {14},
     number = {2},
     year = {2010},
     url = {http://geodesic.mathdoc.fr/item/JGG_2010_14_2_JGG_2010_14_2_a4/}
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S. Stamatakis; H. Al-Zoubi . Surfaces of Revolution Satisfying ΔIIIx = Ax. Journal for geometry and graphics, Tome 14 (2010) no. 2, pp. 181-186. http://geodesic.mathdoc.fr/item/JGG_2010_14_2_JGG_2010_14_2_a4/