A Geometric Application of Soliton Surfaces Associated with The Betchov–Da Rios Equation Using an Extended Darboux Frame Field in E4

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dc.contributor.authorKazan, Ahmet
dc.contributor.authorAltin, Mustafa
dc.date.accessioned2026-06-19T06:31:55Z
dc.date.available2026-06-19T06:31:55Z
dc.date.issued2025
dc.departmentMalatya Turgut Özal Üniversitesi
dc.description.abstractIn this paper, for a soliton surface Ω = Ω(u, v) associated with the Betchov–Da Rios equation, we obtain the derivative formulae of an extended Darboux frame field of a unit speed u-parameter curve Ω = Ω(u, v) for all v. Also, we get the geometric invariants k and h of the soliton surface Ω = Ω(u, v) and we obtain the Gaussian curvature, mean curvature vector and Gaussian torsion of Ω. We give some important geometric characterizations such as flatness, minimality and semi-umbilicaly with the aid of these invariants. Additionally, we study the curvature ellipse of the Betchov–Da Rios soliton surface and Wintgen ideal (superconformal) Betchov–Da Rios soliton surface with respect to an extended Darboux frame field. Finally, we construct an application for the Betchov–Da Rios soliton surface with the aid of an extended Darboux frame field. © 2025 Polish Scientific Publishers
dc.identifier.doi10.1016/S0034-4877(25)00011-4
dc.identifier.endpage92
dc.identifier.issn0034-4877
dc.identifier.issue1
dc.identifier.scopus2-s2.0-105000606502
dc.identifier.scopusqualityQ2
dc.identifier.startpage71
dc.identifier.urihttps://doi.org/10.1016/S0034-4877(25)00011-4
dc.identifier.urihttps://hdl.handle.net/20.500.12899/4865
dc.identifier.volume95
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherElsevier Ltd
dc.relation.ispartofReports on Mathematical Physics
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_Scopus_20260612
dc.subjectBetchov–Da Rios Equation
dc.subjectCurvature Ellipse
dc.subjectExtended Darboux Frame
dc.subjectWintgen Inequality
dc.titleA Geometric Application of Soliton Surfaces Associated with The Betchov–Da Rios Equation Using an Extended Darboux Frame Field in E4
dc.typeArticle

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