Curvature, Harnack's inequality, and a spectral characterization of nilmanifolds
type: Item
instance of: scholarly article
title: Curvature, Harnack's inequality, and a spectral characterization of nilmanifolds
zbMATH Open document ID: 1026.58021
DOI: 10.1023/A:1022888232095
author: Erwann Aubry
author: Bruno Colbois
author: Patrick Ghanaat
author: Ernst A. Ruh
published in: Annals of Global Analysis and Geometry
publication date: 2003-06-09T00:00:00Z
review text: Generalizing a classical result of Bochner, which asserts that the \(n\)-torus is the only \(n\)-dimensional Riemannian manifold with positive semidefinite Ricci tensor and first Betti number equal to \(n\), the authors give sufficient conditions for a Riemannian manifold to be a nilmanifold or an infra-nilmanifold. Their hypothesis involves both bounds on the Ricci tensor for some integral norm and on the eigenvalues of the Laplacian acting on \(1\)-forms. The proof relies on some Harnack-type inequality.
reviewed by: Jean-François Quint
Mathematics Subject Classification ID: 58J50
Mathematics Subject Classification ID: 53C20
zbMATH DE Number: 1924865
zbMATH Keywords: Harnack inequality
zbMATH Keywords: nilmanifolds
zbMATH Keywords: Laplacian
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1924865