Translation Surfaces in Euclidean 3-Space

Authors: Muhammed Çetin, Yılmaz Tunçer, Nejat Ekmekçi

Abstract:

In this paper, the translation surfaces in 3-dimensional Euclidean space generated by two space curves have been investigated. It has been indicated that Scherk surface is not only minimal translation surface.

Keywords: Minimal surface, Surface of Scherk, Translationsurface

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1072283

References:

[1] D. W. Yoon, "On the Gauss map of translation surfaces in Minkowski 3- space," Taiwanese Journal of Mathematics, vol. 6, no. 3, pp. 389-398, 2002.
[2] H. Liu, "Translation surfaces with constant mean curvature in 3- dimensional spaces," Journal of Geometry, vol. 64, pp. 141-149, 1999.
[3] L. Verstraelen, J. Walrave, and S. Yaprak, "The minimal translation surfaces in Euclidean space," Soochow Journal of Mathematics, vol. 20, no. 1, pp. 77-82, 1994.
[4] M. Munteanu, and A. I. Nistor, "On the geometry of the second fundamental form of translation surfaces in E3, arXiv:0812.3166v1
[math.DG] 16 Dec. 2008.