On Riemannian 3-manifolds with distinct constant Ricci eigenvalues
type: Item
instance of: scholarly article
title: On Riemannian 3-manifolds with distinct constant Ricci eigenvalues
zbMATH Open document ID: 0813.53020
DOI: 10.1007/BF01450473
author: Friedbert Prüfer
author: Oldřich Kowalski
published in: Mathematische Annalen
publication date: 1994-11-09T00:00:00Z
full work available at URL: https://eudml.org/doc/165239
review text: A 3-dimensional Riemannian manifold \((M,g)\) is curvature homogeneous if and only if the eigenvalues \(\rho_ i\), \(i=1,2,3\), of the Ricci endomorphism are constant. The classification of this class of spaces has been treated by the first author for the case \(\rho_ 1= \rho_ 2 \neq\rho_ 3\) and a lot of examples are given. For the case of different Ricci eigenvalues, Yamato provided already some explicit complete examples on \(\mathbb{R}^ 3\) and the first author gave some modified noncomplete examples. Moreover, Spiro and Tricerri proved the existence of such spaces for each triplet of prescribed distinct constant Ricci eigenvalues by using the technique of formally integrable differentiable systems but they did not provide explicit solutions. In the present paper the authors also prove this existence but now by providing explicit examples for every choice of \(\rho_ 1> \rho_ 2> \rho_ 3\).
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 53C30
zbMATH DE Number: 683130
zbMATH Keywords: curvature homogeneous
zbMATH Keywords: Ricci endomorphism
zbMATH Keywords: Ricci eigenvalues
Wikidata QID: Q115393502
reviewed by: Lieven Vanhecke
MaRDI profile type: Publication
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OpenAlex ID: W205501734
description: scientific article; zbMATH DE number 683130