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

  • Baba-Hamed, Chahrazede ;
  • Bekkar, Mohammed
  • Received : 2011.06.14
  • Published : 2013.07.31

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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Cited by

  1. Helicoidal surfaces satisfying $${\Delta ^{II}\mathbf{G}=f(\mathbf{G}+C)}$$ Δ II G = f ( G + C ) vol.107, pp.3, 2016, https://doi.org/10.1007/s00022-015-0284-0