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O(p + 1) × O(q + 1)-invariant (r – 1)-minimal hypersurfaces in Euclidean space
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Paulo Sousa
Published/Copyright:
February 1, 2010
Abstract
The aim of the paper is to present a classification of nonextendable immersed O(p+1) × O(q + 1)-invariant (r – 1)-minimal hypersurfaces in the Euclidean space 
, with p, q > 1 and 2 ≤ r ≤ 1 min{p, q}, by analyzing embeddedness as well as (r – 1)-stability. The case r = 1 and r = 2 were treated in [Alencar, Trans. Amer. Math. Soc. 337: 129–141, 1993] and [Sato, de Souza Neto, Ann. Global Anal. Geom. 29: 221–240, 2006], respectively. Generalizing the seminal work of Bombieri et al. we also present a (r – 1)-stable complete embedded hypersurface of with Hr = 0 and O(p + 1) × O(q + 1)-invariant, where p + q ≥ r + 5, that is not homeomorphic to 
.
Received: 2007-10-30
Revised: 2008-12-26
Published Online: 2010-02-01
Published in Print: 2010-January
© de Gruyter 2010
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- Secant dimensions of low-dimensional homogeneous varieties
- Peano differentiable extensions in o-minimal structures
- Global properties of codimension two spacelike submanifolds in Minkowski space
- Local recognition of the line graph of an anisotropic vector space
- Bicanonical map of surfaces with χ = 1 fibered by hyperelliptic curves of genus 3
- O(p + 1) × O(q + 1)-invariant (r – 1)-minimal hypersurfaces in Euclidean space
- Positivity in power series rings
- Scrolls over four dimensional varieties
- Nearly flag-transitive affine planes
Articles in the same Issue
- Secant dimensions of low-dimensional homogeneous varieties
- Peano differentiable extensions in o-minimal structures
- Global properties of codimension two spacelike submanifolds in Minkowski space
- Local recognition of the line graph of an anisotropic vector space
- Bicanonical map of surfaces with χ = 1 fibered by hyperelliptic curves of genus 3
- O(p + 1) × O(q + 1)-invariant (r – 1)-minimal hypersurfaces in Euclidean space
- Positivity in power series rings
- Scrolls over four dimensional varieties
- Nearly flag-transitive affine planes
