dc.contributor.author | Bektaş, Özcan | |
dc.contributor.author | Gürses, Nurten Bayrak | |
dc.contributor.author | Yüce, Salim | |
dc.date.accessioned | 2020-12-19T19:51:10Z | |
dc.date.available | 2020-12-19T19:51:10Z | |
dc.date.issued | 2016 | |
dc.identifier.citation | Bektas, O., Gurses, N.B., Yuce, S. (2016). Quaternionic osculating curves in Euclidean and semi-Euclidean space. Journal of Dynamical Systems and Geometric Theories, 14(1), 65-84. https://doi.org/10.1080/1726037X.2016.1177935 | en_US |
dc.identifier.issn | 1726-037X | |
dc.identifier.issn | 2169-0057 | |
dc.identifier.uri | https://doi.org/10.1080/1726037X.2016.1177935 | |
dc.identifier.uri | https://hdl.handle.net/11436/2513 | |
dc.description | GURSES, NURTEN/0000-0001-8407-854X | en_US |
dc.description | WOS: 000382505200005 | en_US |
dc.description.abstract | In this study, the osculating curves in Euclidean space E-3 and E-4, well known in differential geometry, are studied through the instrumentality of quaternions. We inoculate sundry delineations for quaternionic osculating curves in the Euclidean space E-3, then we portray the quaternionic osculating curve in E-4 as a quaternionic curve whose position vector every time reclines in the orthogonal complement N1/2 (or N1/3) of its first binormal vector field N-2 (or N-3), where {T,N-1,N-2,N-3} be the Frenet instrumentations of the quaternionic curve in the Euclidean space E-4. We feature quaternionic osculating curves from the point of view their curvature functions K, k and (r K) and serve the necessary and the sufficient conditions for arbitrary quaternionic curve in E-4 to be a quaternionic osculating. Moreover, we gain an explicit equation of a quaternionic osculating curve in E-4. in the last two section, we described quaternionic osculating curves in the semi-Euclidean space and some theorems are testified. | en_US |
dc.language.iso | eng | en_US |
dc.publisher | Taylor & Francis Ltd | en_US |
dc.rights | info:eu-repo/semantics/closedAccess | en_US |
dc.subject | 11R52 | en_US |
dc.subject | 53A04 | en_US |
dc.subject | 53C50 | en_US |
dc.subject | Osculating curve | en_US |
dc.subject | Frenet equations | en_US |
dc.subject | Curvature | en_US |
dc.subject | Real quaternion | en_US |
dc.title | Quaternionic osculating curves in Euclidean and semi-Euclidean space | en_US |
dc.type | article | en_US |
dc.contributor.department | RTEÜ, Fen - Edebiyat Fakültesi, Matematik Bölümü | en_US |
dc.contributor.institutionauthor | Bektaş, Özcan | |
dc.identifier.doi | 10.1080/1726037X.2016.1177935 | |
dc.identifier.volume | 14 | en_US |
dc.identifier.issue | 1 | en_US |
dc.identifier.startpage | 65 | en_US |
dc.identifier.endpage | 84 | en_US |
dc.relation.journal | Journal of Dynamical Systems and Geometric Theories | en_US |
dc.relation.publicationcategory | Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı | en_US |