Sweeping Surfaces Due to Conjugate Bishop Frame in 3-Dimensional Lie Group

In this work, we present a new Bishop frame for the conjugate curve of a curve in the 3-dimensional Lie group G3. With the help of this frame, we derive a parametric representation for a sweeping surface and show that the parametric curves on this surface are curvature lines. We then examine the loc...

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Bibliographic Details
Published inSymmetry (Basel) Vol. 15; no. 4; p. 910
Main Authors Al-Jedani, Awatif, Abdel-Baky, Rashad
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.04.2023
Subjects
Conjugates
Convexity
curvature line
Design
developable surface
Geometry
Lie groups
parabolic points
profile curve
Sweeping
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Summary:In this work, we present a new Bishop frame for the conjugate curve of a curve in the 3-dimensional Lie group G3. With the help of this frame, we derive a parametric representation for a sweeping surface and show that the parametric curves on this surface are curvature lines. We then examine the local singularities and convexity of this sweeping surface and establish the sufficient and necessary conditions for it to be a developable ruled surface. Additionally, we provide detailed explanations and examples of its applications.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym15040910