Frenet Curves in Euclidean 4-Space

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dc.contributor.authorDeshmukh, Sharief
dc.contributor.authorAl-Dayel, Ibrahim
dc.contributor.authorIlarslan, Kazim
dc.date.accessioned2020-06-25T18:22:40Z
dc.date.available2020-06-25T18:22:40Z
dc.date.issued2017
dc.departmentKırıkkale Üniversitesi
dc.descriptionDeshmukh, Sharief/0000-0003-3700-8164
dc.description.abstractIn this paper, we study rectifying curves arising through the dilation of unit speed curves on the unit sphere S-3 and conclude that arcs of great circles on S-3 do not dilate to rectifying curves, which develope previously obtained results for rectifying curves in Eucidean spaces. This fact allows us to prove that there exists an associated rectifying curve for each Frenet curve in the Euclidean space E-4 and a result of the fact rectifying curves in the Euclidean space E-4 are ample, indeed as an appication, we present an ordinary differential equation satisfied by the distance function of a Frenet curve in E-4 which alows us to characterize the spherical curves and rectifying curves in E-4. Furthermore, we study ccr-curves in the Euclidean space E-4 which are generalizations of helices in E-3 and show that the property of a helix that its tangent vector field makes a constant angel with a fixed vector (axis of helix) does not go through for a ccr-curve.en_US
dc.identifier.citationclosedAccessen_US
dc.identifier.endpage66en_US
dc.identifier.issn1307-5624
dc.identifier.issue2en_US
dc.identifier.startpage56en_US
dc.identifier.urihttps://hdl.handle.net/20.500.12587/6854
dc.identifier.volume10en_US
dc.identifier.wosWOS:000416507200007
dc.identifier.wosqualityN/A
dc.indekslendigikaynakWeb of Science
dc.language.isoen
dc.publisherInt Electronic Journal Geometryen_US
dc.relation.ispartofInternational Electronic Journal Of Geometry
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectFrenet curvesen_US
dc.subjectrectifying curvesen_US
dc.subjectChen curvesen_US
dc.subjectccr-curvesen_US
dc.subjectcurvaturesen_US
dc.titleFrenet Curves in Euclidean 4-Spaceen_US
dc.typeArticle

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