Simultaneous characterizations of partner ruled surfaces using Flc frame

Yanlin Li; Kemal Eren; Kebire Hilal Ayvacı; Soley Ersoy; Yanlin Li; Kemal Eren; Kebire Hilal Ayvacı; Soley Ersoy

doi:10.3934/math.20221106

AIMS Mathematics

2022, Volume 7, Issue 11: 20213-20229. doi: 10.3934/math.20221106

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Research article

Simultaneous characterizations of partner ruled surfaces using Flc frame

1.
School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China
2.
Department of Mathematics, Faculty of Arts and Sciences, Sakarya University, Sakarya 54050, Turkey
3.
Department of Mathematics, Faculty of Arts and Sciences, Ordu University, Ordu, Turkey

Received: 19 July 2022 Revised: 29 August 2022 Accepted: 01 September 2022 Published: 16 September 2022
MSC : 53A04, 53A05

In this study, we introduce partner ruled surfaces according to the Flc frame that is defined on a polynomial curve. First, the conditions of each couple of two partner ruled surfaces to be simultaneously developable and minimal are investigated. Then, the asymptotic, geodesic and curvature lines of the parameter curves of the partner ruled surfaces are simultaneously characterized. Finally, the examples of the partner ruled surfaces are given, and their graphs are drawn.
- Flc frame,
- partner ruled surface,
- geodesic curve,
- asymptotic curve,
- polynomial curves
Citation: Yanlin Li, Kemal Eren, Kebire Hilal Ayvacı, Soley Ersoy. Simultaneous characterizations of partner ruled surfaces using Flc frame[J]. AIMS Mathematics, 2022, 7(11): 20213-20229. doi: 10.3934/math.20221106

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Abstract

In this study, we introduce partner ruled surfaces according to the Flc frame that is defined on a polynomial curve. First, the conditions of each couple of two partner ruled surfaces to be simultaneously developable and minimal are investigated. Then, the asymptotic, geodesic and curvature lines of the parameter curves of the partner ruled surfaces are simultaneously characterized. Finally, the examples of the partner ruled surfaces are given, and their graphs are drawn.

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