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


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.

Cite this article

Francesco Mercuri, Fabio Podestà, José A. P. Seixas, Ruy Tojeiro, Cohomogeneity one hypersurfaces of Euclidean Spaces. Comment. Math. Helv. 81 (2006), no. 2, pp. 471–479

DOI 10.4171/CMH/59