JournalscmhVol. 81 , No. 2DOI 10.4171/cmh/59

Cohomogeneity one hypersurfaces of Euclidean Spaces

  • Francesco Mercuri

    IMECC - UNICAMP, Campinas, Brazil
  • Fabio Podestà

    Universita di Firenze, Italy
  • José A. P. Seixas

    Universidade Federal de Alagoas, Maceió, Brazil
  • Ruy Tojeiro

    Ufscar, São Carlos, Brazil
Cohomogeneity one hypersurfaces of Euclidean Spaces cover


We study isometric immersions f:MnRn+1f: M^{n}\to \mathbb{R}^{n+1} into Euclidean space of dimension n+1n+1 of a complete Riemannian manifold of dimension nn on which a compact connected group of intrinsic isometries acts with principal orbits of codimension one. We give a complete classification if either n3n\geq 3 and MnM^n is compact or if n5n\geq 5 and the connected components of the flat part of MnM^n are bounded. We also provide several sufficient conditions for ff to be a hypersurface of revolution.