Geodesic
Surfaces of Revolution Satisfying ΔIIIx = Ax
Journal for geometry and graphics, Tome 14 (2010) no. 2, pp. 181-186 Cet article a éte moissonné depuis la source Heldermann Verlag

Voir la notice de l'article

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 
@article{JGG_2010_14_2_JGG_2010_14_2_a4,
     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},
     year = {2010},
     volume = {14},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JGG_2010_14_2_JGG_2010_14_2_a4/}
}
TY  - JOUR
AU  - S. Stamatakis
AU  - H. Al-Zoubi 
TI  - Surfaces of Revolution Satisfying ΔIIIx = Ax
JO  - Journal for geometry and graphics
PY  - 2010
SP  - 181
EP  - 186
VL  - 14
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/JGG_2010_14_2_JGG_2010_14_2_a4/
ID  - JGG_2010_14_2_JGG_2010_14_2_a4
ER  - 
%0 Journal Article
%A S. Stamatakis
%A H. Al-Zoubi 
%T Surfaces of Revolution Satisfying ΔIIIx = Ax
%J Journal for geometry and graphics
%D 2010
%P 181-186
%V 14
%N 2
%U http://geodesic.mathdoc.fr/item/JGG_2010_14_2_JGG_2010_14_2_a4/
%F JGG_2010_14_2_JGG_2010_14_2_a4
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/