Ruled and quadric surfaces of finite Chen-type

In this paper, we study ruled surfaces and quadrics in the 3-dimensional Euclidean space which are of finite \(III\)-type, that is, they are of finite type, in the sense of B.-Y. Chen, with respect to the third fundamental form. We show that helicoids and spheres are the only ruled and quadric surfa...

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Bibliographic Details
Published in:arXiv.org 2022-02
Main Authors: Al-Zoubi, Hassan, Stamatakis, Stylianos, Almimi, Hani
Format: Article
Language:English
Subjects:
Euclidean geometry
Euclidean space
Online Access:Get full text
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Summary:In this paper, we study ruled surfaces and quadrics in the 3-dimensional Euclidean space which are of finite \(III\)-type, that is, they are of finite type, in the sense of B.-Y. Chen, with respect to the third fundamental form. We show that helicoids and spheres are the only ruled and quadric surfaces of finite \(III\)-type, respectively.
ISSN:2331-8422