Publication:
A generalization of the notion of helix

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10.55730_1300-0098.3418_paper.pdf(1.26 MB)
Date
2023
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Authors
Lucas Saorín, Pascual ; Ortega Yagües, José Antonio
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Publisher
Scientific and Technological Research Council of Turkey
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Matemáticas
DOI
https://doi.org/10.55730/1300-0098.3418
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info:eu-repo/semantics/article
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Abstract
In this paper we generalize the notion of helix in the three-dimensional Euclidean space, which we define as that curve $\alpha$ for which there is an $F$-constant vector field $W$ along $\alpha$ that forms a constant angle with a fixed direction $V$ (called an axis of the helix). We find the natural equation and the geometric integration of helices $\alpha$ where the $F$-constant vector field $W$ is orthogonal to its axis.
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Helix , Osculating helix , Normal helix , Rectifying helix , $F$-constant vector field , Darboux vector
Citation
Turkish Journal of Mathematics, Vol. 47 (4), pp. 1158-1168
URI
http://hdl.handle.net/10201/164729
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