Space curves related by a transformation of combescure

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dc.authorid0000-0002-0122-559Xen_US
dc.authorscopusid7005108545en_US
dc.authorwosidERM-3196-2022en_US
dc.contributor.authorCamcı, Çetin
dc.contributor.authorUcum, Ali
dc.contributor.authorIlarslan, Kazım
dc.date.accessioned2023-05-16T06:21:39Z
dc.date.available2023-05-16T06:21:39Z
dc.date.issued2021en_US
dc.departmentFakülteler, Fen Fakültesi, Matematik Bölümü
dc.description.abstractIn this paper, the curves associated with the Combescure transform are discussed. With the help of the fact that these curves have a common Frenet frame, an equivalence relation is defined. The equivalence classes obtained by this equivalence relation have been examined for some special curves and it has been obtained that all curves in the equivalence class of a helix curve are also helix curves. This is also true for k-slant helix curves. The important part of this paper consists of the useful construction method to obtain a curve from the given curve a with the help of Combescure transformation. With this method, some special curves such as Bertrand, Mannheim, Salkowski, anti-Salkowski or spherical curve can be obtained from any curve related by a Combescure transform. For example, we obtain an example of Mannheim curves explicitly obtained from an anti-Salkowski curve. It is not easy to find an example of Mannheim curves except circular helix in the literature. In general, the conditions for being Bertrand, Mannheim, Salkowski, anti-Salkowski or spherical curve of the curve beta obtained from the given curve alpha with the help of Combescure transformation were obtained.en_US
dc.identifier.citationCamcı, Ç., Ucum, A. & Ilarslan, K. (2021). Space curves related by a transformation of combescure. Journal of Dynamical Systems and Geometric Theories, 19(2), 271-287. doi: 10.1080/1726037X.2021.2011113en_US
dc.identifier.doi10.1080/1726037X.2021.2011113
dc.identifier.endpage287en_US
dc.identifier.issn1726-037X
dc.identifier.issn2169-0057
dc.identifier.issue2en_US
dc.identifier.startpage271en_US
dc.identifier.urihttps://doi.org/10.1080/1726037X.2021.2011113
dc.identifier.urihttps://hdl.handle.net/20.500.12428/4156
dc.identifier.volume19en_US
dc.identifier.wosWOS:000738792700006
dc.identifier.wosqualityN/A
dc.indekslendigikaynakWeb of Science
dc.institutionauthorCamcı, Çetin
dc.language.isoen
dc.publisherTaylor and Francis Ltd.en_US
dc.relation.ispartofJournal of Dynamical Systems and Geometric Theoriesen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectCombescure transformationen_US
dc.subjectParallel Frenet framesen_US
dc.subjectBertrand curvesen_US
dc.subjectMannheim curvesen_US
dc.subjectHelixen_US
dc.subjectSpherical curveen_US
dc.subjectSalkowski and anti-Salkowski curvesen_US
dc.titleSpace curves related by a transformation of combescure
dc.typeArticle

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