On Riemannian manifolds with \(\epsilon\)-maximal diameter and bounded curvature
type: Item
instance of: scholarly article
title: On Riemannian manifolds with \(\epsilon\)-maximal diameter and bounded curvature
zbMATH Open document ID: 0764.53036
DOI: 10.1007/BF02571808
published in: Mathematische Zeitschrift
publication date: 1993-03-03T00:00:00Z
full work available at URL: https://eudml.org/doc/174413
review text: We study closed Riemannian \(n\)-manifolds \(M\) with \(\varepsilon\)-maximal diameter, i.e. \(\text{Ric}(M)\geq n-1\) and \(\pi- \text{diam}(M)\leq\varepsilon\). We show that there exist two positive numbers \(\varepsilon=\varepsilon(n)\) and \(C(n)\), such that if a closed \(n\)-manifold \(M\) with sectional curvature \(K_ M\geq -K\), \(K>0\), has \(\varepsilon K^{-n/2}\)-maximal diameter, then the total Betti number of \(M\), \(\sum^ n_{i=0} b_ i(M)\), is bounded by \(C(n)\).
Mathematics Subject Classification ID: 53C20
zbMATH DE Number: 126393
zbMATH Keywords: closed Riemannian \(n\)-manifolds
zbMATH Keywords: total Betti number
Wikidata QID: Q115391981
author: Zhongmin Shen
MaRDI profile type: Publication
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OpenAlex ID: W1965489232
description: scientific article; zbMATH DE number 126393