Abstract
<abstract><p>In the present paper, we describe dual translation surfaces in the Galilean 3-space having the constant Gaussian and mean curvatures as well as Weingarten and linear Weingarten dual translation surfaces. We also study dual translation surfaces in $ \mathbb{G}_{3} $ under the condition $ \Delta ^{II}r = \lambda _{i}r_{i} $, where $ \lambda _{i}\in R $ and $ \Delta ^{II} $ denotes the Laplacian operator respect to the second fundamental form.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
Reference15 articles.
1. H. Scherk, Bemerkungen über die kleinste Fläche innerhalb gegebener Grenzen, J. Reine Angew. Math., 1835 (1835), 185–208. http://dx.doi.org/10.1515/crll.1835.13.185
2. K. Arslan, B. Bayram, B. Bulca, G. Ozturk, On translation surfaces in 4-dimensional Euclidean space, Acta Comment. Univ. Ta., 20 (2016), 123–133. http://dx.doi.org/10.12697/ACUTM.2016.20.11
3. B. Bulca, On generalized LN-Surfaces in $\mathbb{E}^{4}$, Mathematical Sciences and Applications E-Notes, 1 (2013), 35–41.
4. A. Cakmak, M. Karacan, S. Kiziltug, D. Yoon, Translation surfaces in the 3 dimensional Galilean space satisfying $\Delta ^IIx_{i} = \lambda _{i}x_{i}$, B. Korean Math. Soc., 54 (2017), 1241–1254. http://dx.doi.org/10.4134/BKMS.b160442
5. F. Dillen, W. Goemans, I. Woestyne, Translation surfaces of Weingarten type in 3-space, Bulletin of the Transilvania University of Brasov, 1 (2008), 1–12.
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