The geometrical properties of the Smarandache curves on 3-dimension pseudo-spheres generated by null curves

Huina Zhang; Yanping Zhao; Jianguo Sun; Huina Zhang; Yanping Zhao; Jianguo Sun

doi:10.3934/math.20241056

AIMS Mathematics

2024, Volume 9, Issue 8: 21703-21730. doi: 10.3934/math.20241056

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The geometrical properties of the Smarandache curves on 3-dimension pseudo-spheres generated by null curves

School of Science, China University of Petroleum (east China), Qingdao, 266555, China

Received: 28 March 2024 Revised: 21 June 2024 Accepted: 28 June 2024 Published: 08 July 2024
MSC : 35A53, 58C20

In this paper, we presented the geometrical properties of Smarandache curves on 3-pseudo-spheres. These curves were examined in the context of the lightcone, de Sitter space, and anti-de Sitter space. By leveraging the curvature relationships between the null curve and its corresponding Smarandache curves, we established necessary and sufficient conditions. Additionally, we illustrated our main results through two examples.
- null curve,
- Smarandache curve,
- slant helix,
- pseudo-spheres
Citation: Huina Zhang, Yanping Zhao, Jianguo Sun. The geometrical properties of the Smarandache curves on 3-dimension pseudo-spheres generated by null curves[J]. AIMS Mathematics, 2024, 9(8): 21703-21730. doi: 10.3934/math.20241056

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Abstract

In this paper, we presented the geometrical properties of Smarandache curves on 3-pseudo-spheres. These curves were examined in the context of the lightcone, de Sitter space, and anti-de Sitter space. By leveraging the curvature relationships between the null curve and its corresponding Smarandache curves, we established necessary and sufficient conditions. Additionally, we illustrated our main results through two examples.

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