On simultaneous characterizations of partner-ruled surfaces in Minkowski 3-space

Yanlin Li; Kemal Eren; Soley Ersoy; Yanlin Li; Kemal Eren; Soley Ersoy

doi:10.3934/math.20231135

AIMS Mathematics

2023, Volume 8, Issue 9: 22256-22273. doi: 10.3934/math.20231135

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Research article

On simultaneous characterizations of partner-ruled surfaces in Minkowski 3-space

1.
School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China
2.
Key Laboratory of Cryptography of Zhejiang Province, Hangzhou Normal University, Hangzhou 311121, China
3.
Sakarya University Technology Developing Zones Manager CO., Sakarya, 54050, Turkey
4.
Department of Mathematics, Faculty of Sciences, Sakarya University, Sakarya 54050, Turkey

Received: 16 May 2023 Revised: 21 June 2023 Accepted: 29 June 2023 Published: 13 July 2023
MSC : 53A04, 53A05

In this study, the partner-ruled surfaces in Minkowski 3-space, which are defined according to the Frenet vectors of non-null space curves, are introduced with extra conditions that guarantee the existence of definite surface normals. First, the requirements of each pair of partner-ruled surfaces to be simultaneously developable and minimal (or maximal for spacelike surfaces) are investigated. The surfaces also simultaneously characterize the asymptotic, geodesic and curvature lines of the parameter curves of these surfaces. Finally, the study provides examples of timelike and spacelike partner-ruled surfaces and includes their graphs.
- partner-ruled surface,
- developable and minimal surface,
- geodesic curve,
- asymptotic curve
Citation: Yanlin Li, Kemal Eren, Soley Ersoy. On simultaneous characterizations of partner-ruled surfaces in Minkowski 3-space[J]. AIMS Mathematics, 2023, 8(9): 22256-22273. doi: 10.3934/math.20231135

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Abstract

In this study, the partner-ruled surfaces in Minkowski 3-space, which are defined according to the Frenet vectors of non-null space curves, are introduced with extra conditions that guarantee the existence of definite surface normals. First, the requirements of each pair of partner-ruled surfaces to be simultaneously developable and minimal (or maximal for spacelike surfaces) are investigated. The surfaces also simultaneously characterize the asymptotic, geodesic and curvature lines of the parameter curves of these surfaces. Finally, the study provides examples of timelike and spacelike partner-ruled surfaces and includes their graphs.

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