Characterizations of space curves with 1-type Darboux instantaneous rotation vector
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2016
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Abstract
In this study, by using Laplace and normal Laplace operators, we give some characterizations for the Darboux instantaneous rotation vector field of the curves in the Euclidean 3-space E3. Further, we give necessary and sufficient conditions for unit speed space curves to have 1-type Darboux vectors. Moreover, we obtain some characterizations of helices according to Darboux vector. © 2016 Korean Mathematical Society.