Circular evolutes and involutes of spacelike framed curves and their duality relations in Minkowski 3-space

Wei Zhang; Pengcheng Li; Donghe Pei; Wei Zhang; Pengcheng Li; Donghe Pei

doi:10.3934/math.2024276

AIMS Mathematics

2024, Volume 9, Issue 3: 5688-5707. doi: 10.3934/math.2024276

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Research article

Circular evolutes and involutes of spacelike framed curves and their duality relations in Minkowski 3-space

1.
School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China
2.
Department of Mathematics, Harbin Institute of Technology, Weihai 264209, China
3.
School of Mathematics and Statistics, Yili Normal University, Yining 835000, China

Received: 30 December 2023 Revised: 16 January 2024 Accepted: 19 January 2024 Published: 30 January 2024
MSC : 53A04, 53A05, 57R45

In the present paper, we defined the circular evolutes and involutes for a given spacelike framed curve with respect to Bishop directions in Minkowski 3-space. Then, we studied the essential duality relations among parallel curves, normal surfaces, and circular evolutes and involutes. Furthermore, we also studied the duality relations of their singularities. Based on these studies, we found that it is crucially important to consider the duality relations among different geometric objects for the research of submanifolds with singularities.
- spacelike framed curves,
- circular evolutes,
- involutes,
- parallel curves,
- normal surfaces
Citation: Wei Zhang, Pengcheng Li, Donghe Pei. Circular evolutes and involutes of spacelike framed curves and their duality relations in Minkowski 3-space[J]. AIMS Mathematics, 2024, 9(3): 5688-5707. doi: 10.3934/math.2024276

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Abstract

In the present paper, we defined the circular evolutes and involutes for a given spacelike framed curve with respect to Bishop directions in Minkowski 3-space. Then, we studied the essential duality relations among parallel curves, normal surfaces, and circular evolutes and involutes. Furthermore, we also studied the duality relations of their singularities. Based on these studies, we found that it is crucially important to consider the duality relations among different geometric objects for the research of submanifolds with singularities.

References

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