Equivalent curves in En

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dc.contributor.authorMollaogullari, Ahmet
dc.contributor.authorGumus, Mehmet
dc.contributor.authorCamci, Didem Karalarlioglu
dc.contributor.authorIlarslan, Kazim
dc.contributor.authorCamci, Cetin
dc.date.accessioned2026-02-03T11:59:46Z
dc.date.available2026-02-03T11:59:46Z
dc.date.issued2025
dc.departmentÇanakkale Onsekiz Mart Üniversitesi
dc.description.abstractIn this paper, we first define an equivalence relation for curves in En. Based on this equivalence relation, we investigate the relationships between the Frenet frame and curvatures of equivalent curves. Next, we introduce the concept of linearly dependent curvatures in Enand examine its implications for equivalent curves. Building on this concept and the proposed equivalence relation, we present a method to construct (1,3)-Bertrand curves in E4. Additionally, we derive the relationships between the harmonic curvatures of equivalent curves and use these relationships to establish several properties of equivalent helical curves. These results enable systematic construction of curves with prescribed geometric properties.
dc.description.sponsorshipCanakkale Onsekiz Mart University The Scientific Research Coordination Unit [FHD-2022-3977]
dc.description.sponsorshipThis work was supported by Canakkale Onsekiz Mart University The Scientific Research Coordination Unit, Project number: FHD-2022-3977.The authors would like to thank the anonymous reviewers for their valuable comments and suggestions, which have greatly improved the quality and clarity of this manuscript.
dc.identifier.doi10.3934/math.2025701
dc.identifier.endpage15662
dc.identifier.issn2473-6988
dc.identifier.issue7
dc.identifier.scopus2-s2.0-105011186322
dc.identifier.scopusqualityQ1
dc.identifier.startpage15653
dc.identifier.urihttps://doi.org/10.3934/math.2025701
dc.identifier.urihttps://hdl.handle.net/20.500.12428/34411
dc.identifier.volume10
dc.identifier.wosWOS:001529635500003
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherAmer Inst Mathematical Sciences-Aims
dc.relation.ispartofAims Mathematics
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_WOS_20260130
dc.subjectcombescure transformation
dc.subjectcurve theory
dc.subjectequivalent curves
dc.subjecthelix
dc.subjectBertrand curve
dc.titleEquivalent curves in En
dc.typeArticle

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