Circular surfaces and singularities in Euclidean 3-space $ \mathbb{E}^{3} $

Nadia Alluhaibi; Nadia Alluhaibi

doi:10.3934/math.2022701

AIMS Mathematics

2022, Volume 7, Issue 7: 12671-12688. doi: 10.3934/math.2022701

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Research article

Circular surfaces and singularities in Euclidean 3-space $ \mathbb{E}^{3} $

Nadia Alluhaibi ^,

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

Received: 16 August 2021 Revised: 16 April 2022 Accepted: 22 April 2022 Published: 28 April 2022
MSC : 53A04, 53A05, 53A17

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.
- lines of curvature and singularity,
- roller coaster surface
Citation: Nadia Alluhaibi. Circular surfaces and singularities in Euclidean 3-space $ \mathbb{E}^{3} $[J]. AIMS Mathematics, 2022, 7(7): 12671-12688. doi: 10.3934/math.2022701

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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.

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