A New Approach on Some Special Curves

Abstract

In this paper, we obtain some characterizations for a Frenet curve with the help of an alternative frame different from Frenet frame. Also, in the present study we consider weak biharmonic and harmonic 1-type curves by using the mean curvature vector field of the curve. We also study 1-type and biharmonic curves whose mean curvature vector field is in the kernel of Laplacian. We give some theorems for them in the Euclidean 3-space. Moreover, we give the classifications of these type curves.

Keywords

• Alternative frame
• harmonic curves
• biharmonic curves

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