On helices and Bertrand curves in Euclidean 3-space
M Babaarslan, Y Yayli - arXiv preprint arXiv:1010.3555, 2010 - arxiv.org
arXiv preprint arXiv:1010.3555, 2010•arxiv.org
In this article, we investigate Bertrand curves corresponding to the spherical images of the
tangent, binormal, principal normal and Darboux indicatrices of a space curve in Euclidean
3-space. As a result, in case of a space curve is a general helix, we show that the curves
corresponding to the spherical images of its the tangent indicatrix and binormal indicatrix are
both Bertrand curves and circular helices. Similarly, in case of a space curve is a slant helix,
we demonstrate that the curve corresponding to the spherical image of its the principal …
tangent, binormal, principal normal and Darboux indicatrices of a space curve in Euclidean
3-space. As a result, in case of a space curve is a general helix, we show that the curves
corresponding to the spherical images of its the tangent indicatrix and binormal indicatrix are
both Bertrand curves and circular helices. Similarly, in case of a space curve is a slant helix,
we demonstrate that the curve corresponding to the spherical image of its the principal …
In this article, we investigate Bertrand curves corresponding to the spherical images of the tangent, binormal, principal normal and Darboux indicatrices of a space curve in Euclidean 3-space. As a result, in case of a space curve is a general helix, we show that the curves corresponding to the spherical images of its the tangent indicatrix and binormal indicatrix are both Bertrand curves and circular helices. Similarly, in case of a space curve is a slant helix, we demonstrate that the curve corresponding to the spherical image of its the principal normal indicatrix is both a Bertrand curve and a circular helix.
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