On 1/4-pinched 4-dimensional Riemannian manifolds of negative curvature
type: Item
instance of: scholarly article
title: On 1/4-pinched 4-dimensional Riemannian manifolds of negative curvature
zbMATH Open document ID: 0575.53020
DOI: 10.1007/BF00130484
author: Marina Ville
published in: Annals of Global Analysis and Geometry
publication date: 1985-01-01T00:00:00Z
review text: The following interesting result is proved using integral formulae for characteristic numbers: Let M be a compact oriented 4-dimensional Riemannian manifold with sectional curvature, \(K_ M\), satisfying \(-1\leq K_ M\leq -1/4\). Then the signature \(\tau\) (M), and Euler characteristic, \(\chi\) (M), are related by \(| \tau (M)| \leq (1/3) \chi (M)\). Moreover, equality holds if and only if M is locally isometric to the complex hyperbolic plane.
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 53C35
zbMATH DE Number: 3919236
zbMATH Keywords: integral formulae
zbMATH Keywords: characteristic numbers
zbMATH Keywords: signature
zbMATH Keywords: Euler characteristic
zbMATH Keywords: complex hyperbolic plane
Wikidata QID: Q115395219
reviewed by: Karsten Grove
MaRDI profile type: Publication
cites work: Q3270944
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cites work: Compact four-dimensional Einstein manifolds
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cites work: Strong Rigidity of Locally Symmetric Spaces. (AM-78)
cites work: Nombres caractéristiques d'une variété riemannienne de dimension 4
description: scientific article; zbMATH DE number 3919236