Generic properties of Darboux-type curves

Jie Huang; Sining Wei; Jie Huang; Sining Wei

doi:10.3934/era.2025210

Electronic Research Archive

2025, Volume 33, Issue 8: 4679-4692. doi: 10.3934/era.2025210

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Research article

Generic properties of Darboux-type curves

Jie Huang ¹,
Sining Wei ^{2
,
,}

1.
School of Mathematical Sciences, Heilongjiang University, Harbin 150000, China
2.
School of Data Science and Articial Intelligence, Dongbei University of Finance and Economics, Dalian 116025, China

Received: 02 June 2025 Revised: 23 July 2025 Accepted: 30 July 2025 Published: 13 August 2025

In this paper, we present a method for constructing Darboux-type curves by using spherical curves and smooth functions. We show that all Darboux-type curves can be generated using this method. We discuss the relationship between Darboux-type curves and rectifying curves. Moreover, we establish a connection between Darboux-type curves and geodesics on a rectifying developable surface from the viewpoint of curves on ruled surfaces.
- Darboux-type curves,
- spherical curves,
- rectifying curves,
- rectifying developable surface,
- geodesics
Citation: Jie Huang, Sining Wei. Generic properties of Darboux-type curves[J]. Electronic Research Archive, 2025, 33(8): 4679-4692. doi: 10.3934/era.2025210

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Abstract

In this paper, we present a method for constructing Darboux-type curves by using spherical curves and smooth functions. We show that all Darboux-type curves can be generated using this method. We discuss the relationship between Darboux-type curves and rectifying curves. Moreover, we establish a connection between Darboux-type curves and geodesics on a rectifying developable surface from the viewpoint of curves on ruled surfaces.

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