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

Nadia Alluhaibi

doi:10.3934/math.2022701

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

Journal article

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Peer reviewed

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

Nadia Alluhaibi

AIMS mathematics, Vol.7(7), pp.12671-12688

2022

DOI: https://doi.org/10.3934/math.2022701

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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Title: Circular surfaces and singularities in Euclidean 3-space $ \mathbb{E}^{3}
Creators - without role: Nadia Alluhaibi
Publication Details: AIMS mathematics, Vol.7(7), pp.12671-12688
Identifiers: 9934476608331
Academic Unit: King Abdulaziz University
Language: English
Resource Type: Journal article