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

https://izlik.org/JA53GT89BM

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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