Concircular helices and concircular surfaces in Euclidean 3-space $\mathbb{R}^{3}$

Year 2023, Volume: 52 Issue: 4, 995 - 1005, 15.08.2023

Pascual Lucas , José Antonio Ortega Yagües

https://doi.org/10.15672/hujms.1187220

Cited By: 1

Abstract

In this paper we characterize concircular helices in $\mathbb{R}^{3}$ by means of a differential equation involving their curvature and torsion. We find a full description of concircular surfaces in $\mathbb{R}^{3}$ as a special family of ruled surfaces, and we show that $M\subset\mathbb{R}^{3}$ 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.

Keywords

generalized helix, slant helix, rectifying curve, concircular helix, generalized cylinder, helix surface, conical surface, concircular surface, tangent surface

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