Publication:
Geodesics, Line of Curvatures and Asymptotic Curves Versus Relaxed Elastic Lines on an Oriented Surface

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dc.contributor.authorBayram, Ergin
dc.contributor.authorKasap, Emin
dc.date.accessioned2020-06-21T13:27:49Z
dc.date.available2020-06-21T13:27:49Z
dc.date.issued2017
dc.departmentOMÜen_US
dc.department-temp[Bayram, Ergin -- Kasap, Emin] Ondokuz Mayis Univ, Fac Arts & Sci, Dept Math, TR-55200 Atakum, Samsun, Turkey --en_US
dc.description.abstractLet alpha(s) be an arc on a connected oriented surface S in E-3, parameterized by arc length s, with curvature k and length l. The total square curvature K of alpha is defined by K=integral(1)(0)kappa(2)The arc alpha is called a relaxed elastic line if it is an extremal for the variational problem of minimizing the value of K within the family of all arcs of length l on S having the same initial point and initial direction as alpha In this study, we show that a geodesic is a relaxed elastic line if and only if it is planar and an asymptotic curve cannot be a relaxed elastic line. Also, we obtain a criterion for a line of curvature to be a relaxed elastic line.en_US
dc.identifier.endpage40en_US
dc.identifier.issn1844-9581
dc.identifier.issue1en_US
dc.identifier.startpage37en_US
dc.identifier.urihttps://hdl.handle.net/20.500.12712/12852
dc.identifier.wosWOS:000401266000004
dc.language.isoenen_US
dc.publisherEditura Bibliotheca-Bibliotheca Publ Houseen_US
dc.relation.journalJournal of Science and Artsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectRelaxed Elastic Lineen_US
dc.subjectGeodesicen_US
dc.subjectLine of Curvatureen_US
dc.subjectAsymptotic Curveen_US
dc.titleGeodesics, Line of Curvatures and Asymptotic Curves Versus Relaxed Elastic Lines on an Oriented Surfaceen_US
dc.typeArticleen_US
dspace.entity.typePublication

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