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Bull. Korean Math. Soc. 2017; 54(4): 1241-1254
Online first article February 1, 2017 Printed July 31, 2017
https://doi.org/10.4134/BKMS.b160442
Copyright © The Korean Mathematical Society.
Translation surfaces in the 3-dimensional Galilean space satisfying $\Delta ^{II}x_{i}=\lambda _{i}x_{i}$
Ali \c{C}akmak, Murat Kemal Karacan, Sezai Kiziltug, and Dae Won Yoon
Bitlis Eren University, Usak University 1 Eylul Campus, Erzincan University, Gyeongsang National University
In this paper, we classify translation surfaces in the three dimensional Galilean space $\mathbb{G}_{3}$ satisfying some algebraic equations in terms of the coordinate functions and the Laplacian operators with respect to the second fundamental form of the surface. We also give explicit forms of these surfaces.
Keywords: Laplace operator, Galilean space, translation surfaces
MSC numbers: 53A35, 53B30, 53A40
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