On Backlund transformation and motion of null Cartan curves

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dc.contributor.authorErdogdu, Melek
dc.contributor.authorYavuz, Ayse
dc.date.accessioned2024-02-23T14:26:26Z
dc.date.available2024-02-23T14:26:26Z
dc.date.issued2022
dc.departmentNEÜen_US
dc.description.abstractThe main scope of this paper is to examine null Cartan curves especially the ones with constant torsion. In accordance with this scope, the position vector of a null Cartan curve is stated by a linear combination of the vector fields of its pseudo-orthogonal frame with differentiable functions. However, the most important difference that distinguishes this study from the other studies is that the Bertrand curve couples (timelike, spacelike or null) of null Cartan curves are also examined. Consequently, it is seen that all kinds of Bertrand couples of a given null Cartan curve with constant curvature functions have also constant curvature functions. This result is the most valuable result of the study, but allows us to introduce a transformation on null Cartan curves. Then, it is proved that aforesaid transformation is a Backlund transformation which is well recognized in modern physics. Moreover, motion of an inextensible null Cartan curve is investigated. By considering time evolution of null Cartan curve, the angular momentum vector is examined. And three different situations are given depending on the character of the angular momentum vector Omega. In the case of tau(t) = 0, we discuss the solution of the system which is obtained by compatibility conditions. Finally, we provide the relation between torsion of the curve and the velocity vector components of the moving curve C.en_US
dc.identifier.doi10.1142/S0219887822500141
dc.identifier.issn0219-8878
dc.identifier.issn1793-6977
dc.identifier.issue1en_US
dc.identifier.scopus2-s2.0-85120428952en_US
dc.identifier.scopusqualityQ3en_US
dc.identifier.urihttps://doi.org/10.1142/S0219887822500141
dc.identifier.urihttps://hdl.handle.net/20.500.12452/14187
dc.identifier.volume19en_US
dc.identifier.wosWOS:000733361600003en_US
dc.identifier.wosqualityQ2en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherWorld Scientific Publ Co Pte Ltden_US
dc.relation.ispartofInternational Journal Of Geometric Methods In Modern Physicsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectNull Cartan Curveen_US
dc.subjectBacklund Transformationen_US
dc.subjectBertrand Curveen_US
dc.subjectMotion Of Inextensible Null Cartan Curveen_US
dc.titleOn Backlund transformation and motion of null Cartan curvesen_US
dc.typeArticleen_US

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