Tubes of coordinate finite type Gauss map in the Euclidean 3-space
Differential Geometry
2019-04-30 v1
Abstract
In this paper, we consider tubes in the Euclidean 3-space whose Gauss map n is of coordinate finite I-type, i.e., the position vector n satisfies the relation {\Delta}In = {\Lambda}n, where {\Delta}I is the Laplace operator with respect to the first fundamental form I of the surface and {\Lambda} is a square matrix of order 3. We show that circular cylinders are the only class of surfaces mentioned above of coordinate finite I-type Gauss map.
Keywords
Cite
@article{arxiv.1904.12339,
title = {Tubes of coordinate finite type Gauss map in the Euclidean 3-space},
author = {Hassan Al-Zoubi and Hamza Alzaareer and Tareq Hamadneh and Mohammad Al Rawajbeh},
journal= {arXiv preprint arXiv:1904.12339},
year = {2019}
}