Translation surfaces in the 3-dimensional Galilean space satisfying $\Delta ^{II}x_{i}=\lambda _{i}x_{i}$
Bull. Korean Math. Soc. 2017 Vol. 54, No. 4, 1241-1254
https://doi.org/10.4134/BKMS.b160442
Published online July 31, 2017
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
Abstract : 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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