Cohomogeneity-One Ruled Hypersurfaces in $\mathbb{CP}^2$ and $\mathbb{C}H^2$

Thomas A. Ivey; Patrick J. Ryan

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arXiv · 2605.22979

Cohomogeneity-One Ruled Hypersurfaces in $\mathbb{CP}^2$ and $\mathbb{C}H^2$

Thomas A. Ivey·Patrick J. Ryan

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Abstract

In this paper, we show how to construct a special class of ruled hypersurfaces in the nonflat complex space forms $\mathbb{CP}^n$ and $\mathbb{C}H^n$. 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.

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BibTeX RIS

Thomas A. Ivey, Patrick J. Ryan. 2026-05-21. Cohomogeneity-One Ruled Hypersurfaces in $\mathbb{CP}^2$ and $\mathbb{C}H^2$. https://arxiv.org/abs/2605.22979

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