Commentarii Mathematici Helvetici


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Volume 81, Issue 2, 2006, pp. 471–479
DOI: 10.4171/CMH/59

Published online: 2006-06-30

Cohomogeneity one hypersurfaces of Euclidean Spaces

Francesco Mercuri[1], Fabio Podestà[2], José A. P. Seixas[3] and Ruy Tojeiro[4]

(1) IMECC - UNICAMP, Campinas, Brazil
(2) Universita di Firenze, Italy
(3) Universidade Federal de Alagoas, Maceió, Brazil
(4) Ufscar, São Carlos, Brazil

We study isometric immersions $f: M^{n}\to \mathbb{R}^{n+1}$ into Euclidean space of dimension $n+1$ of a complete Riemannian manifold of dimension $n$ on which a compact connected group of intrinsic isometries acts with principal orbits of codimension one. We give a complete classification if either $n\geq 3$ and $M^n$ is compact or if $n\geq 5$ and the connected components of the flat part of $M^n$ are bounded. We also provide several sufficient conditions for $f$ to be a hypersurface of revolution.

Keywords: Cohomogeneity one manifolds, hypersurfaces

Mercuri Francesco, Podestà Fabio, Seixas José, Tojeiro Ruy: Cohomogeneity one hypersurfaces of Euclidean Spaces. Comment. Math. Helv. 81 (2006), 471-479. doi: 10.4171/CMH/59