On Helices and Bertrand Curves in Euclidean 3-Space

Details On Helices and Bertrand Curves in Euclidean 3-Space On Helices and Bertrand Curves in Euclidean 3-Space

2010-10-18

arxiv.org/abs/1010.3555v4

Mathematics

Differential Geometry

10 pages, 3 figures

Scientific paper

In this article, we investigate Bertrand curves corresponding to spherical images of the tangent indicatrix, binormal indicatrix, principal normal indicatrix and Darboux indicatrix of a space curve in Euclidean 3-space. As a result, in case of a space curve is general helix, we show that curve corresponding to spherical images of its tangent indicatrix and binormal indicatrix are circular helices and Bertrand curves. Similarly, in case of a space curve is slant helix, we demonstrate that the curve corresponding to spherical image of its principal normal indicatrix is circular helix and Bertrand curve.

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