On four-dimensional Einstein affine hyperspheres
type: Item
instance of: scholarly article
title: On four-dimensional Einstein affine hyperspheres
zbMATH Open document ID: 1356.53013
author: Haizhong Li
author: Luc Vrancken
author: Zejun Hu
published in: Differential Geometry and its Applications
publication date: 2016-12-28T00:00:00Z
review text: The authors classify the 4-dimensional locally strongly convex affine hyperspheres whose affine metrics are Einstein. They prove the following: Theorem. Let \(x: M^4\to \mathbb R^5\) be a locally strongly convex affine hypersphere with its affine metric being Einstein, then it is locally affine equivalent to the open part of either one of the hyperquadrics, or the hyperbolic affine hypersphere \(Q(1, 4): x^1x^2x^3x^4x^5 = 1\), where \((x^1, \dots, x^5)\) are the coordinates of \(\mathbb R^5\).
Mathematics Subject Classification ID: 53A15
Mathematics Subject Classification ID: 53B25
Mathematics Subject Classification ID: 53C25
zbMATH DE Number: 6668717
zbMATH Keywords: affine hypersphere
zbMATH Keywords: affine metric
zbMATH Keywords: Einstein metric
reviewed by: Huili Liu
MaRDI profile type: Publication
full work available at URL: j.difgeo.2016.10.003
OpenAlex ID: W2553973664
Wikidata QID: Q115355597
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DOI: 10.1016/J.DIFGEO.2016.10.003
description: scientific article; zbMATH DE number 6668717