Construction of the spacelike constant angle surface family in Minkowski 3-space

Cai-Yun Li; Chun-Gang Zhu; Cai-Yun Li; Chun-Gang Zhu

doi:10.3934/math.2020408

AIMS Mathematics

2020, Volume 5, Issue 6: 6341-6354. doi: 10.3934/math.2020408

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Research article

Construction of the spacelike constant angle surface family in Minkowski 3-space

Cai-Yun Li ¹,
Chun-Gang Zhu ^{2
,
,}

1.
School of Mathematical and Physical Sciences, Dalian University of Technology, Panjin 124221, China
2.
School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China

Received: 05 June 2020 Accepted: 31 July 2020 Published: 10 August 2020
MSC : 53A07

A spacelike constant angle surface in $E_1^3$ (Minkowski 3-space) is defined by its unit normal vector field forms a constant angle with some fixed vector direction. In this paper, we use the Frenet frame to express the surface and construct a family of spacelike constant angle surfaces which possess the given curve as isoparametric curve. The normal vector of each surface forms a constant angle with a fixed vector lying in the spacelike cone and in the timelike cone respectively. Finally, we give some representative examples.
- Minkowski space,
- constant angle surface,
- spacelike cone,
- timelike cone
Citation: Cai-Yun Li, Chun-Gang Zhu. Construction of the spacelike constant angle surface family in Minkowski 3-space[J]. AIMS Mathematics, 2020, 5(6): 6341-6354. doi: 10.3934/math.2020408

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Abstract

A spacelike constant angle surface in $E_1^3$ (Minkowski 3-space) is defined by its unit normal vector field forms a constant angle with some fixed vector direction. In this paper, we use the Frenet frame to express the surface and construct a family of spacelike constant angle surfaces which possess the given curve as isoparametric curve. The normal vector of each surface forms a constant angle with a fixed vector lying in the spacelike cone and in the timelike cone respectively. Finally, we give some representative examples.

References

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