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http://dx.doi.org/10.4134/BKMS.2013.50.4.1061

SURFACES OF REVOLUTION SATISFYING ΔIIG = f(G + C)  

Baba-Hamed, Chahrazede (Department of Mathematics Faculty of Sciences University of Oran)
Bekkar, Mohammed (Department of Mathematics Faculty of Sciences University of Oran)
Publication Information
Bulletin of the Korean Mathematical Society / v.50, no.4, 2013 , pp. 1061-1067 More about this Journal
Abstract
In this paper, we study surfaces of revolution without parabolic points in 3-Euclidean space $\mathbb{R}^3$, satisfying the condition ${\Delta}^{II}G=f(G+C)$, where ${\Delta}^{II}$ is the Laplace operator with respect to the second fundamental form, $f$ is a smooth function on the surface and C is a constant vector. Our main results state that surfaces of revolution without parabolic points in $\mathbb{R}^3$ which satisfy the condition ${\Delta}^{II}G=fG$, coincide with surfaces of revolution with non-zero constant Gaussian curvature.
Keywords
surfaces of revolution; Laplace operator; pointwise 1-type Gauss map; second fundamental form;
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Times Cited By KSCI : 5  (Citation Analysis)
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