Patrick J. Ryan

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20242026

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math.DG2026

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

Thomas A. Ivey, Patrick J. Ryan

In this paper, we show how to construct a special class of ruled hypersurfaces in the nonflat complex space forms $CP^{n}$ and $C H^{n}$ . This is done by taking an arb…

math.DG2026

On Cartan's Examples of Isoparametric Hypersurfaces and Their Focal Submanifolds

Thomas E. Cecil, Patrick J. Ryan

This paper is a survey of Cartan's examples of isoparametric hypersurfaces in spheres and their focal submanifolds that were described in his fundamental work on the subject, which…

math.DG2025

Tight Spherical Embeddings (Updated Version)

Thomas E. Cecil, Patrick J. Ryan

This is an updated version of a paper which appeared in the proceedings of the 1979 Berlin Colloquium on Global Differential Geometry. This paper contains the original exposition t…

math.DG2024

On the Work of Cartan and MÃ¼nzner on Isoparametric Hypersurfaces

Thomas E. Cecil, Patrick J. Ryan

A hypersurface $M^{n}$ in a real space form $R^{n + 1}$ , $S^{n + 1}$ , or $H^{n + 1}$ is isoparametric if it has constant principal curvatures. This paper is a survey of the fundament…

Cohomogeneity-One Ruled Hypersurfaces in CP2 and CH2

On Cartan's Examples of Isoparametric Hypersurfaces and Their Focal Submanifolds

Tight Spherical Embeddings (Updated Version)

On the Work of Cartan and MÃ¼nzner on Isoparametric Hypersurfaces

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