Concircular hypersurfaces and concircular helices in space forms
Differential Geometry
2026-01-27 v1
Abstract
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.
Keywords
Cite
@article{arxiv.2601.18003,
title = {Concircular hypersurfaces and concircular helices in space forms},
author = {Pascual Lucas and José Antonio Ortega-Yagües},
journal= {arXiv preprint arXiv:2601.18003},
year = {2026}
}