Concircular helices and concircular surfaces in Euclidean 3-space R3
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911402170515456 |
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| author | Lucas, Pascual Ortega-Yagües, José Antonio |
| author_facet | Lucas, Pascual Ortega-Yagües, José Antonio |
| contents | In this paper we characterize concircular helices in $R^3$ by means of a differential equation involving their curvature and torsion. We find a full description of concircular surfaces in $R^3$ as a special family of ruled surfaces, and we show that $M$ in $R^3$ 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_19252 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Concircular helices and concircular surfaces in Euclidean 3-space R3 Lucas, Pascual Ortega-Yagües, José Antonio Differential Geometry 53A04, 53A05 In this paper we characterize concircular helices in $R^3$ by means of a differential equation involving their curvature and torsion. We find a full description of concircular surfaces in $R^3$ as a special family of ruled surfaces, and we show that $M$ in $R^3$ 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. |
| title | Concircular helices and concircular surfaces in Euclidean 3-space R3 |
| topic | Differential Geometry 53A04, 53A05 |
| url | https://arxiv.org/abs/2601.19252 |