Some Characterizations of Isotropic Curves In the Euclidean Space
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چکیده
The curves, of which the square of the distance between the two points equal to zero, are called minimal or isotropic curves [4]. In this work, first, necessary and sufficient conditions to be a Pseudo Helix, which is a special case of such curves, are presented. Thereafter, it is proven that an isotropic curve’s position vector and pseudo curvature satisfy a vector differential equation of fourth order. Additionally, In view of solution of mentioned equation, position vector of pseudo helices is obtained. Keywords—Classical Differential Geometry, Euclidean space, Minimal Curves, Isotropic Curves, Pseudo Helix.
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