Bulletin of the Belgian Mathematical Society - Simon Stevin

Slant helices in the Euclidean 3-space revisited

Pascual Lucas and José Antonio Ortega-Yagües

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Abstract

In this paper, we study the surfaces whose geodesics are slant curves. We show that a unit speed curve $\gamma$ in the 3-dimensional Euclidean space is a slant helix if and only if it is a geodesic of a helix surface. We prove that the striction line of a helix surface is a general helix; as a consequence, slant helices are characterized as geodesics of the tangent surface of a general helix. Finally, we provide two methods for constructing slant helices in helix surfaces.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 23, Number 1 (2016), 133-150.

Dates
First available in Project Euclid: 9 March 2016

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1457560859

Digital Object Identifier
doi:10.36045/bbms/1457560859

Mathematical Reviews number (MathSciNet)
MR3471984

Zentralblatt MATH identifier
1336.53004

Subjects
Primary: 53A04: Curves in Euclidean space 53A05: Surfaces in Euclidean space

Keywords
slant helix helix surface general helix tangent surface

Citation

Lucas, Pascual; Ortega-Yagües, José Antonio. Slant helices in the Euclidean 3-space revisited. Bull. Belg. Math. Soc. Simon Stevin 23 (2016), no. 1, 133--150. doi:10.36045/bbms/1457560859. https://projecteuclid.org/euclid.bbms/1457560859


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