Darboux helices in three dimensional Lie groups

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.

Keywords

• curves in lie groups
• slant helix
• angular velocity vector
• darboux helix