Isoparametric Hypersurfaces of $\mathbb H^n\times\mathbb R$ and $\mathbb S^n\times\mathbb R$

Ronaldo F. de Lima; Giuseppe Pipoli

Isoparametric Hypersurfaces of $\mathbb H^n\times\mathbb R$ and $\mathbb S^n\times\mathbb R$

Differential Geometry 2025-11-04 v2

Authors: Ronaldo F. de Lima , Giuseppe Pipoli

Abstract

We classify the isoparametric hypersurfaces and the homogeneous hypersurfaces of $\mathbb H^n\times\mathbb R$ and $\mathbb S^n\times\mathbb R$ , $n\ge 2$ , by establishing that any such hypersurface has constant angle function and constant principal curvatures.

Keywords

isoparametric hypersurfaces homogeneous hypersurfaces principal curvatures constant angle function differential geometry

Cite

@article{arxiv.2411.11506,
  title  = {Isoparametric Hypersurfaces of $\mathbb H^n\times\mathbb R$ and $\mathbb S^n\times\mathbb R$},
  author = {Ronaldo F. de Lima and Giuseppe Pipoli},
  journal= {arXiv preprint arXiv:2411.11506},
  year   = {2025}
}

Comments

28 pages, 1 figure. To appear in Annali della Scuola Normale Superiore di Pisa

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