Special ball-homogeneous spaces
type: Item
instance of: scholarly article
title: Special ball-homogeneous spaces
zbMATH Open document ID: 0892.53023
DOI: 10.4171/ZAA/792
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 1998-08-03T00:00:00Z
review text: A ball-homogeneous space is a Riemannian manifold \((M,g)\) on which the volumes of all sufficiently small geodesic balls only depend on the radius. In dimensions greater than two, it is an open problem whether each ball-homogeneous Riemannian manifold is locally homogeneous. In the present paper a positive answer is given in the following special situations: (a) \(M\) is three-dimensional with at most two distinct Ricci eigenvalues; (b) \(M\) is three-dimensional and its Ricci tensor is either a Codazzi tensor, or it is cyclic parallel; (c) \(M\) is conformally flat with at most three distinct Ricci eigenvalues (and of arbitrary dimension).
reviewed by: Oldřich Kowalski
Mathematics Subject Classification ID: 53C30
Mathematics Subject Classification ID: 53C25
Mathematics Subject Classification ID: 53C35
zbMATH DE Number: 1129172
zbMATH Keywords: conformal flatness
zbMATH Keywords: ball-homogeneous space
zbMATH Keywords: Ricci tensor
zbMATH Keywords: distinct Ricci eigenvalues
author: Giovanni Calvaruso
author: Lieven Vanhecke
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.4171/zaa/792
OpenAlex ID: W1970494905
description: scientific article; zbMATH DE number 1129172