SPACE CURVES RELATED BY A TRANSFORMATION OF COMBESCURE

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dc.contributor.authorCamci, Cetin
dc.contributor.authorUcum, Ali
dc.contributor.authorIlarslan, Kazim
dc.date.accessioned2025-01-21T16:44:29Z
dc.date.available2025-01-21T16:44:29Z
dc.date.issued2021
dc.departmentKırıkkale Üniversitesi
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.
dc.identifier.doi10.1080/1726037X.2021.2011113
dc.identifier.endpage287
dc.identifier.issn1726-037X
dc.identifier.issn2169-0057
dc.identifier.issue2
dc.identifier.startpage271
dc.identifier.urihttps://doi.org/10.1080/1726037X.2021.2011113
dc.identifier.urihttps://hdl.handle.net/20.500.12587/25470
dc.identifier.volume19
dc.identifier.wosWOS:000738792700006
dc.identifier.wosqualityN/A
dc.indekslendigikaynakWeb of Science
dc.language.isoen
dc.publisherTaylor & Francis Ltd
dc.relation.ispartofJournal of Dynamical Systems and Geometric Theories
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.snmzKA_20241229
dc.subjectCombescure transformation; Parallel Frenet frames; Bertrand curves; Mannheim curves; Helix; Spherical curve; Salkowski and anti-Salkowski curves
dc.titleSPACE CURVES RELATED BY A TRANSFORMATION OF COMBESCURE
dc.typeArticle

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