PreprintCC BY 4.0arXiv
Cohomogeneity-One Ruled Hypersurfaces in ℂℙ2 and ℂH2
Abstract
In this paper, we show how to construct a special class of ruled hypersurfaces in the nonflat complex space forms ℂℙn and ℂHn. This is done by taking an arbitrary smooth curve in a totally geodesic (complex) one-dimensional submanifold and erecting an orthogonal ruling over each of its points. Concentrating on the n=2 case, we also examine the special situation in which the base curve has constant geodesic curvature. We show that, in this case, the construction yields precisely the real-analytic hypersurfaces of cohomogeneity one that satisfy a certain transversality condition.
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BibTeX
@misc{ivey2026cohomogeneityone,
title = {{Cohomogeneity-One Ruled Hypersurfaces in $\mathbbCP^2$ and $\mathbbCH^2$}},
author = {Thomas A. Ivey and Patrick J. Ryan},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.22979},
eprint = {2605.22979},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.22979},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Cohomogeneity-One Ruled Hypersurfaces in ℂℙ^2 and ℂH^2
AU - Thomas A. Ivey
AU - Patrick J. Ryan
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2605.22979
UR - https://arxiv.org/abs/2605.22979
AB - In this paper, we show how to construct a special class of ruled hypersurfaces in the nonflat complex space forms ℂℙ^n and ℂH^n. This is done by taking an arbitrary smooth curve in a totally geodesic (complex) one-dimensional submanifold and erecting an orthogonal ruling over each of its points. Concentrating on the n=2 case, we also examine the special situation in which the base curve has constant geodesic curvature. We show that, in this case, the construction yields precisely the real-analytic hypersurfaces of cohomogeneity one that satisfy a certain transversality condition.
ER -