Curve-Surface Pairs on Embedded Surfaces and Involute D-Scroll of the Curve-Surface Pair in E3

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dc.authoridSENYURT, Suleyman/0000-0003-1097-5541
dc.contributor.authorKaya, Filiz Ertem
dc.contributor.authorSenyurt, Suleyman
dc.date.accessioned2024-11-07T13:34:29Z
dc.date.available2024-11-07T13:34:29Z
dc.date.issued2024
dc.departmentNiğde Ömer Halisdemir Üniversitesi
dc.description.abstractWillmore defined embedded surfaces on f:S -> E-3, which is the embedding of S into Euclidean 3-space. He investigated the Euclidean metric of E-3, inducing a Riemannian structure on f(S). The expression analogous to the left-hand member of the curvature K is replaced by the mean curvature H-2 on f(S). Our aim is to observe the Gaussian and mean curvatures of curve-surface pairs using embedded surfaces in different curve-surface pairs and to define some developable operations on their curve-surface pairs. We also investigate the embedded surfaces using the Willmore method. We first recall the Darboux curve-surface and derive the new characterizations. This curve-surface pair is called the osculating Darboux curve-surface if its position vector always lies in the osculating Darboux plane spanned by a Darboux frame. Thus, we observed an osculating Darboux curve-surface pair. We also obtained the D-scroll of the curve-surface pair and involute D-scroll of the curve-surface pair with some differential geometric elements and found D(alpha,M)(s) and D*(alpha,M)(s)-scrolls of the curve-surface pair (alpha,M).
dc.identifier.doi10.3390/sym16030323
dc.identifier.issn2073-8994
dc.identifier.issue3
dc.identifier.scopus2-s2.0-85188957370
dc.identifier.scopusqualityQ2
dc.identifier.urihttps://doi.org/10.3390/sym16030323
dc.identifier.urihttps://hdl.handle.net/11480/16012
dc.identifier.volume16
dc.identifier.wosWOS:001193464500001
dc.identifier.wosqualityN/A
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherMdpi
dc.relation.ispartofSymmetry-Basel
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_20241106
dc.subjectcurve-surface pair
dc.subjectembedded
dc.subjectcurvatures
dc.subjectGaussian curvature
dc.subjectmean curvature
dc.subjectosculating Darboux frame
dc.titleCurve-Surface Pairs on Embedded Surfaces and Involute D-Scroll of the Curve-Surface Pair in E3
dc.typeArticle

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