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

Authors : Pascual LUCAS, José Antonio ORTEGA YAGÜES

Pages : 995-1005

Doi:10.15672/hujms.1187220

View : 183 | Download : 234

Publication Date : 2023-08-15

Article Type : Research Paper

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