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Research Article | Open Access

Circular surfaces and singularities in Euclidean 3-space E 3

Department of mathematics, College of Science and Arts, King Abdulaziz University, Rabigh, Saudi Arabia
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Abstract

The approach of the paper is on circular surfaces. A circular surface is a one-parameter family of standard circles with fixed radius regarding a curve, which acts as the spine curve. In the study, we have parametrized circular surfaces and have provided its geometric properties like singularities and striction curves comparing with those of ruled surfaces. Furthermore, we have addressed the conditions of minimality of roller coaster surfaces. Meanwhile, we support the results of the approach by some examples.

Keywords

lines of curvature and singularityroller coaster surface
CLC number: 53A04, 53A05, 53A17

References

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AIMS Mathematics
Volume 7 Issue 7,
July 2022
Pages 12671-12688
DOI: 10.3934/math.2022701

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Cite this article:
Alluhaibi N. Circular surfaces and singularities in Euclidean 3-space E 3 . AIMS Mathematics, 2022, 7(7): 12671-12688. https://doi.org/10.3934/math.2022701

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Received: 16 August 2021
Revised: 16 April 2022
Accepted: 22 April 2022
Published: 15 July 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)