Codazzi tensors with two eigenvalue functions
type: Item
instance of: scholarly article
title: Codazzi tensors with two eigenvalue functions
zbMATH Open document ID: 1282.53013
DOI: 10.1090/S0002-9939-2013-11616-3
author: Gabe Merton
published in: Proceedings of the American Mathematical Society
publication date: 2013-08-30T00:00:00Z
full work available at URL: https://arxiv.org/abs/1111.7002
Mathematics Subject Classification ID: 53A45
Mathematics Subject Classification ID: 53B20
zbMATH DE Number: 6203454
zbMATH Keywords: Codazzi tensor
zbMATH Keywords: Riemannian manifold
MaRDI profile type: Publication
arXiv ID: 1111.7002
cites work: Some decompositions of the space of symmetric tensors on a Riemannian manifolds
cites work: Q4720334
cites work: Les variétés de dimension 4 à signature non nulle dont la courbure est harmonique sont d'Einstein
cites work: Codazzi Tensor Fields, Curvature and Pontryagin Forms
cites work: Krümmungsflächen von isometrischen Immersionen in Räume konstanter Krümmung
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review text: The author ``addresses a gap in the classification of Codazzi tensors with exactly two eigenfunctions on a Riemannian manifold of dimension three or higher.'' NEWLINENEWLINENEWLINEFirst, he improves a result by Derdzinski, who proved that ``if the trace of a Codazzi tensor is constant and the dimension of one of the eigenspaces is \(n-1\), then the metric is a warped product, where the base is an open interval''.NEWLINENEWLINEMoreover, the author exhibits examples of Codazzi tensors which disprove a claim by A. L. Besse that the ``warped product conclusion holds without any restriction on the trace.''
reviewed by: Marco Modugno
description: scientific article; zbMATH DE number 6203454