Journal of Prime Research in Mathematics

Vol. 18 (2022), Issue 1, pp. 96 – 107
ISSN: 1817-3462E (Online) 1818-5495 (Print)

Quadrics with finite Chen-type Gauss map

Hamza Alzaareer\(^{a,*}\), Hassan Al-Zoubi\(^a\), Farhan Abdel-Fattah\(^b\)

\(^a\)Department of Mathematics, Al-Zaytoonah University of Jordan, P.O. Box 130, Amman, Jordan 11733.

\(^b\)Department of Cyber Security, Al-Zaytoonah University of Jordan, P.O. Box 130, Amman, Jordan 11733.

Correspondence should be addressed to: : h.alzaareer@zuj.edu.jo

Copyright © 2022 Hamza Alzaareer, Hassan Al-Zoubi, Farhan Abdel-Fattah . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Published: Received: : 23 January 2022; Accepted: 09 July 2022; Published Online: 22 August 2022.

Abstract

In this article, we investigate the family of quadric surfaces in E³ according to its finite type Gauss map.We prove that spheres, circular cylinders, and planes are the only quadric surfaces with finite Chen type Gauss map corresponding to the first fundamental form I

Keywords:

Surfaces of finite Chen-type, Surfaces in the Euclidean 3-space, Beltrami-Laplace operator,Quadric surfaces.