On Ricci eigenvalues of locally homogeneous Riemann 3-manifolds
type: Item
instance of: scholarly article
title: On Ricci eigenvalues of locally homogeneous Riemann 3-manifolds
zbMATH Open document ID: 0859.53034
DOI: 10.1007/BF00240002
published in: Geometriae Dedicata
publication date: 1997-04-15T00:00:00Z
review text: A 3-dimensional Riemannian manifold \((M^3,g)\) is curvature homogeneous if and only if the principal Ricci curvatures \(\rho_i\), \(i=1,2,3\), are constant. Locally homogeneous \((M^3,g)\) are trivially curvature homogeneous. While there always exist curvature homogeneous \((M^3,g)\) with an arbitrary given triplet \((\rho_1,\rho_2,\rho_3)\), \(\rho_i\in \mathbb{R}\), it follows from the well-known Milnor results that this is not the case for locally homogeneous \((M^3,g)\). The main purpose of the paper is to determine the exact ranges of all triplets \((\rho_1,\rho_2,\rho_3) \in \mathbb{R}^3\) which can occur as Ricci eigenvalues of locally homogeneous \((M^3,g)\).
Mathematics Subject Classification ID: 53C30
zbMATH DE Number: 929908
zbMATH Keywords: locally homogeneous Riemann three-manifolds
zbMATH Keywords: Ricci eigenvalues
author: Oldřich Kowalski
author: Stana Nikčević
reviewed by: Lieven Vanhecke
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00240002
OpenAlex ID: W2087237200
description: scientific article; zbMATH DE number 929908