Translation Surfaces in the 3-Dimensional Pseudo-Galilean Space Satisfying: $\boldsymbol{\bigtriangleup^{\mathrm{II}}\, r_i=\lambda_i r_i}$

Azzi Ahmed; Bekkar Mohammed; Zoubir Hanifi

doi:10.26713/cma.v12i2.1384

Authors

Azzi Ahmed Department of Mathematics and Computer Science, University Centre Ali Kafi, Tindouf, Algeria; Department of Mathematics, Faculty of Sciences, University of Oran 1, Ahmed Benbella, Algeria
Bekkar Mohammed Department of Mathematics and Computer Science, National Polytechnic School of Oran, B.P. 1523 El M'Naour, Oran
Zoubir Hanifi Department of Mathematics, Faculty of Sciences, University of Oran 1, Ahmed Benbella

DOI:

https://doi.org/10.26713/cma.v12i2.1384

Keywords:

Pseudo-Galilean space, Surface of finite type, Translation surfaces, II-Harmonic, Laplacian operator with respect to the second fundamental form

Abstract

In this paper, we classify translation surfaces in a $3$-dimensional Pseudo-Galilean space $\mathbb{G}_{3}^1$ under the condition $\bigtriangleup^{\rm II}\, r_i=\lambda_i r_i$, where $r_i$ are the components of the position vector, $\lambda_i\in\mathbb{R}$, $(i=1,2,3)$, and $\bigtriangleup^{\rm II}$ denotes the Laplace operator with respect to the second fundamental form.

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