### AIMS Mathematics

2020, Issue 4: 3169-3181. doi: 10.3934/math.2020204
Research article

# Darboux helices in three dimensional Lie groups

• 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.

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

### Related Papers:

• 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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