Darboux helices in three dimensional Lie groups
In this paper, we introduce Darboux helices in a three dimensional Lie group G with a bi-invariant metric and give some characterizations of Darboux helices. Besides, we give some relations between some special curves (general helices and slant helices) and Darboux helices. Moreover, we prove that a...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2020-04-01
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| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/10.3934/math.2020204/fulltext.html |
| _version_ | 1811292403280117760 |
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| author | Ufuk Öztürk Zeynep Büşra Alkan |
| author_facet | Ufuk Öztürk Zeynep Büşra Alkan |
| author_sort | Ufuk Öztürk |
| collection | DOAJ |
| description | In this paper, we introduce Darboux helices in a three dimensional Lie group G with a bi-invariant metric and give some characterizations of Darboux helices. Besides, we give some relations between some special curves (general helices and slant helices) and Darboux helices. Moreover, we prove that all Darboux helices are not a slant helix if G is commutative. |
| first_indexed | 2024-04-13T04:44:57Z |
| format | Article |
| id | doaj.art-447f0906f1ef4fed87798946bd361941 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-13T04:44:57Z |
| publishDate | 2020-04-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-447f0906f1ef4fed87798946bd3619412022-12-22T03:01:52ZengAIMS PressAIMS Mathematics2473-69882020-04-01543169318110.3934/math.2020204Darboux helices in three dimensional Lie groupsUfuk Öztürk0Zeynep Büşra Alkan1Department of Mathematics, Faculty of Science, University of Çankırı Karatekin, 18100 Çankırı, TurkeyDepartment of Mathematics, Faculty of Science, University of Çankırı Karatekin, 18100 Çankırı, TurkeyIn this paper, we introduce Darboux helices in a three dimensional Lie group G with a bi-invariant metric and give some characterizations of Darboux helices. Besides, we give some relations between some special curves (general helices and slant helices) and Darboux helices. Moreover, we prove that all Darboux helices are not a slant helix if G is commutative.https://www.aimspress.com/article/10.3934/math.2020204/fulltext.htmlcurves in lie groupsslant helixangular velocity vectordarboux helix |
| spellingShingle | Ufuk Öztürk Zeynep Büşra Alkan Darboux helices in three dimensional Lie groups AIMS Mathematics curves in lie groups slant helix angular velocity vector darboux helix |
| title | Darboux helices in three dimensional Lie groups |
| title_full | Darboux helices in three dimensional Lie groups |
| title_fullStr | Darboux helices in three dimensional Lie groups |
| title_full_unstemmed | Darboux helices in three dimensional Lie groups |
| title_short | Darboux helices in three dimensional Lie groups |
| title_sort | darboux helices in three dimensional lie groups |
| topic | curves in lie groups slant helix angular velocity vector darboux helix |
| url | https://www.aimspress.com/article/10.3934/math.2020204/fulltext.html |
| work_keys_str_mv | AT ufukozturk darbouxhelicesinthreedimensionalliegroups AT zeynepbusraalkan darbouxhelicesinthreedimensionalliegroups |