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Research Article | Open Access

Generic properties of Darboux-type curves

Jie Huang1, Sining Wei2( )
School of Mathematical Sciences, Heilongjiang University, Harbin 150000, China
School of Data Science and Articial Intelligence, Dongbei University of Finance and Economics, Dalian 116025, China
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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.

Keywords

Darboux-type curvesspherical curvesrectifying curvesrectifying developable surfacegeodesics

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Electronic Research Archive
Volume 33 Issue 8,
August 2025
Pages 4679-4692
DOI: 10.3934/era.2025210

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Huang J, Wei S. Generic properties of Darboux-type curves. Electronic Research Archive, 2025, 33(8): 4679-4692. https://doi.org/10.3934/era.2025210

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Received: 02 June 2025
Revised: 23 July 2025
Accepted: 30 July 2025
Published: 13 August 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)