Tubes of coordinate finite type Gauss map in the Euclidean 3-space

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...

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Bibliographic Details
Published in:arXiv.org 2019-04
Main Authors: Al-Zoubi, Hassan, Hamza Alzaareer, Hamadneh, Tareq, Mohammad Al Rawajbeh
Format: Article
Language:English
Subjects:
Circular cylinders
Euclidean geometry
Tubes
Online Access:Get full text
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Summary: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.
ISSN:2331-8422