Isometry groups of Riemannian manifolds with bounded norms
type: Item
instance of: scholarly article
title: Isometry groups of Riemannian manifolds with bounded norms
zbMATH Open document ID: 1119.53025
author: Seong-Hun Paeng
published in: Tôhoku Mathematical Journal. Second Series
publication date: 2006-12-04T00:00:00Z
full work available at URL: tohokumathjen.html
review text: A classical theorem of \textit{S.~Bochner} implies that the isometry group of a compact Riemannian manifold with negative Ricci curvature is finite. In [Duke Math. J. 76, No. 1, 59--73 (1994; Zbl 0820.53045)] \textit{X.~Dai, Z. Shen} and \textit{G.~Wei} improved this by showing that there is a bound depending on geometric data and on the order of the isometry group of a compact manifold with negative Ricci curvature. In this paper the author generalizes these results using integral bounds on Ricci curvature and the concept of norm of a Riemannian manifold introduced by \textit{P. Petersen} [Riemannian geometry. 2nd ed. Graduate Texts in Mathematics 171, Springer, (New York) (2006; Zbl 1220.53002)].
reviewed by: Simon L. Kokkendorff
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 53C21
zbMATH DE Number: 5076982
zbMATH Keywords: Ricci curvature
zbMATH Keywords: isometry group
zbMATH Keywords: norm of manifold
MaRDI profile type: Publication
OpenAlex ID: W1989901882
Wikidata QID: Q115227293
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DOI: 10.2748/TMJ/1156256401
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description: scientific article; zbMATH DE number 5076982