Publication:
Concircular helices and concircular surfaces in Euclidean 3-space R3

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10.15672_hujms.1187220_paper.pdf(1.65 MB)
Date
2023
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Authors
Lucas Saorín, Pascual ; Ortega Yagües, José Antonio
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Publisher
Universidad de Hacettepe
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Matemáticas
DOI
https://doi.org/10.15672/hujms.1187220
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info:eu-repo/semantics/article
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Abstract
In this paper we characterize concircular helices in R3 by means of a differential equation involving their curvature and torsion. We find a full description of concircular surfaces in R3 as a special family of ruled surfaces, and we show that M ⊂ R3 is a proper concircular surface if and only if either M is parallel to a conical surface or M is the normal surface to a spherical curve. Finally, we characterize the concircular helices as geodesics of concircular surfaces.
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Slant helix , Rectifying curve , Concircular helix , Generalized cylinder e , Helix surface , Conical surface , Concircular surface , Tangent surfac , Generalized helix
Citation
Hacettepe Journal of Mathematics and Statistics, 2023, Vol. 52 (4), pp. 995-1005
URI
http://hdl.handle.net/10201/164749
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