Concircular hypersurfaces and concircular helices in space forms
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914280091156480 |
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| author | Lucas, Pascual Ortega-Yagües, José Antonio |
| author_facet | Lucas, Pascual Ortega-Yagües, José Antonio |
| contents | In this paper, we find a full description of concircular hypersurfaces in space forms as a special family of ruled hypersurfaces. We also characterize concircular helices in 3-dimensional space forms by means of a differential equation involving the concircular factor and their curvature and torsion, and we show that the concircular helices are precisely the geodesics of the concircular surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_18003 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Concircular hypersurfaces and concircular helices in space forms Lucas, Pascual Ortega-Yagües, José Antonio Differential Geometry 53A04, 53A05 In this paper, we find a full description of concircular hypersurfaces in space forms as a special family of ruled hypersurfaces. We also characterize concircular helices in 3-dimensional space forms by means of a differential equation involving the concircular factor and their curvature and torsion, and we show that the concircular helices are precisely the geodesics of the concircular surfaces. |
| title | Concircular hypersurfaces and concircular helices in space forms |
| topic | Differential Geometry 53A04, 53A05 |
| url | https://arxiv.org/abs/2601.18003 |