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SURFACES OF REVOLUTION SATISFYING Δ<sup>II</sup>G = f(G + C)
Baba-Hamed, Chahrazede,Bekkar, Mohammed Korean Mathematical Society 2013 대한수학회보 Vol.50 No.4
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.
SURFACES OF REVOLUTION SATISFYING △IIG = f(G + C)
Chahrazede Baba-Hamed,Mohammed Bekkar 대한수학회 2013 대한수학회보 Vol.50 No.4
In this paper, we study surfaces of revolution without par- abolic points in 3-Euclidean space R3, satisfying the condition △IIG = f(G+ C), where △II is the Laplace operator with respect to the second fundamental form, f is a smooth function on the surface and C is a con- stant vector. Our main results state that surfaces of revolution without parabolic points in R3 which satisfy the condition △IIG = fG, coincide with surfaces of revolution with non-zero constant Gaussian curvature.