• Kyungpook Mathematical Journal
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• v.58 no.2
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• pp.377-388
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• 2018

In this paper, we define new quaternionic associated curves called quaternionic principal-direction curves and quaternionic principal-donor curves. We give some properties and relationships between Frenet vectors and curvatures of these curves. For spatial quaternionic curves, we give characterizations for quaternionic helices and quaternionic slant helices by means of their associated curves.

• Honam Mathematical Journal
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• v.34 no.3
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• pp.381-390
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• 2012

In this paper, we give some characterizations for a quaternionic general helix by means of curvatures of a curve in a 4-dimensional Euclidean space.