Stability of \(O(p+1) \times O(p+1)\)-invariant hypersurfaces with zero scalar curvature in Euclidean space
type: Item
instance of: scholarly article
title: Stability of \(O(p+1) \times O(p+1)\)-invariant hypersurfaces with zero scalar curvature in Euclidean space
zbMATH Open document ID: 1036.53039
DOI: 10.1023/A:1019536730847
author: Jocelino Sato
published in: Annals of Global Analysis and Geometry
publication date: 2002-09-18T00:00:00Z
review text: The author classifies \(O(p+1)\times O(p+1)-\)invariant hypersurfaces with zero scalar curvature in \({\mathbb R}^{2p+2},p>1\) according to their profile curves and shows that there are complete and embedded examples. Then, by studying the Morse indices of complete examples, the author shows that there exists a nonplanar globally stable, embedded complete hypersurface with zero scalar curvature in \({\mathbb R}^{2p+2}.\) This stable example provides a counterexample in odd dimensions \(\geq 9\) to a Bernstein-type conjecture for immersions with zero scalar curvature.
reviewed by: Sung-Eun Koh
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53A10
zbMATH DE Number: 1802371
zbMATH Keywords: equivariant geometry
zbMATH Keywords: scalar curvature
zbMATH Keywords: stability
zbMATH Keywords: Bernstein's conjecture
MaRDI profile type: Publication
full work available at URL: a:1019536730847
OpenAlex ID: W253879368
description: scientific article; zbMATH DE number 1802371