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New type direction curves in 3-dimensional compact Lie group. (English) Zbl 1423.53004

Summary: In this paper, new types of associated curves, which are defined as rectifying-direction, osculating-direction, and normal-direction, in a three-dimensional Lie group \(G\) are achieved by using the general definition of the associated curve, and some characterizations for these curves are obtained. Additionally, connections between the new types of associated curves and the curves, such as helices, general helices, Bertrand, and Mannheim, are given.

MSC:

53A04 Curves in Euclidean and related spaces
22E15 General properties and structure of real Lie groups
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