3-dimensional Riemannian metrics with prescribed Ricci principal curvatures
type: Item
instance of: scholarly article
title: 3-dimensional Riemannian metrics with prescribed Ricci principal curvatures
zbMATH Open document ID: 0851.53022
author: Yanyan Li
published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série
publication date: 1996-12-02T00:00:00Z
review text: The authors prove that, for any triplet of distinct constants \(\rho_1\), \(\rho_2\), \(\rho_3\), there always exists an analytic Riemannian metric on a domain of \(\mathbb{R}^3\) whose principal Ricci curvatures are constant and equal to the numbers \(\rho_i\). The local equivalence of such metrics is studied and it is proved that the moduli space of their isometry classes depends on an infinite number of parameters. A more recent result by the reviewer and Z. Vlášek says that the moduli space is parametrized by three arbitrary functions of two variables.
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 58D27
zbMATH DE Number: 891041
zbMATH Keywords: moduli space of isometry classes
zbMATH Keywords: principal Ricci curvatures
reviewed by: Oldřich Kowalski
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 891041