Darboux helices in three dimensional Lie groups

Ufuk Öztürk; Zeynep Büşra Alkan; Ufuk Öztürk; Zeynep Büşra Alkan

doi:10.3934/math.2020204

AIMS Mathematics

2020, Volume 5, Issue 4: 3169-3181. doi: 10.3934/math.2020204

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Research article

Darboux helices in three dimensional Lie groups

Ufuk Öztürk ^,,
Zeynep Büşra Alkan

Department of Mathematics, Faculty of Science, University of Çankırı Karatekin, 18100 Çankırı, Turkey

Received: 04 December 2019 Accepted: 04 March 2020 Published: 26 March 2020
MSC : 22E15, 53A04, 53C40

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.
- curves in Lie groups,
- slant helix,
- angular velocity vector,
- Darboux helix
Citation: Ufuk Öztürk, Zeynep Büşra Alkan. Darboux helices in three dimensional Lie groups[J]. AIMS Mathematics, 2020, 5(4): 3169-3181. doi: 10.3934/math.2020204

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Abstract

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.

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