Quantcast

Affine translation surfaces in the isotropic 3-space

Research paper by Muhittin Evren Aydin, Mahmut Ergut

Indexed on: 07 Nov '16Published on: 07 Nov '16Published in: arXiv - Mathematics - Differential Geometry



Abstract

The isotropic 3-space \mathbb{I}^{3} is a real affine 3-space endowed with the metric dx^{2}+dy^{2}. In this paper we describe Weingarten and linear Weingarten affine translation surfaces in \mathbb{I}^{3}. Further we classify the affine translation surfaces in \mathbb{I}^{3} that satisfy certain equations in terms of the position vector and the Laplace operator.