New examples of complete hypersurfaces with constant positive scalar curvature in the Euclidean space
type: Item
instance of: scholarly article
title: New examples of complete hypersurfaces with constant positive scalar curvature in the Euclidean space
zbMATH Open document ID: 1208.53063
author: Takashi Okayasu
published in: Journal of the Mathematical Society of Japan
publication date: 2011-01-12T00:00:00Z
review text: For complete 2-dimensional surfaces \(M\) in the 3-dimensional Euclidean space \(E^3\) with constant Gaussian curvature, it is well known that \(M\) is a sphere, a plane or a cylinder. For complete \(n\)-dimensional hypersurfaces (\(n\geq 3\)) with constant scalar curvature, the known examples are flat hypersurfaces, spheres, generalized cylinders, some rotational hypersurfaces and some complete hypersurfaces with constant non positive scalar curvature. In this paper, the author constructs a new family of noncompact complete hypersurfaces in \(E^{n+1}\) with constant positive scalar curvature by the method of equivariant differential geometry.
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53C42
zbMATH DE Number: 5835138
zbMATH Keywords: scalar curvature
zbMATH Keywords: equivariant differential geometry
reviewed by: Huili Liu
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/06241137
OpenAlex ID: W2020365897
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DOI: 10.2969/JMSJ/06241137
description: scientific article; zbMATH DE number 5835138