Liu, Huili; Jung, Seoung Dal Affine translation surfaces with constant mean curvature in Euclidean 3-space. (English) Zbl 1380.53011 J. Geom. 108, No. 2, 423-428 (2017). Summary: Using classical methods and solving certain differential equations we classify a kind of new surface, affine translation surfaces, which has the non-zero constant mean curvature in three dimensional Euclidean space \(\mathbf E^3\). Therefore a kind of solutions for the constant mean curvature equation is given. Cited in 5 Documents MSC: 53A05 Surfaces in Euclidean and related spaces 53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature 53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) Keywords:constant mean curvature equation; affine translation surface; mean curvature; surface with non-zero constant mean curvature PDFBibTeX XMLCite \textit{H. Liu} and \textit{S. D. Jung}, J. Geom. 108, No. 2, 423--428 (2017; Zbl 1380.53011) Full Text: DOI References: [1] Kenmotsu, K.: Surfaces with Constant Mean Curvature, Translations of Math. Monographs, vol. 221. American Mathematical Society, Providence (2003) · Zbl 1042.53001 [2] Kenmotsu K.: Surfaces of revolution with periodic mean curvature. Osaka J. Math. 40(3), 687-696 (2003) · Zbl 1041.53005 [3] Liu, H., Yu, Y.: Affine translation surfaces in Euclidean 3-space. In: Proceedings of the Japan Academy, Ser. A, Mathematical Sciences, vol. 89, pp. 111-113, Ser. A (2013) · Zbl 1287.53004 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.