The isometry groups of manifolds of nonpositive curvature with finite volume
type: Item
instance of: scholarly article
title: The isometry groups of manifolds of nonpositive curvature with finite volume
zbMATH Open document ID: 0554.53029
DOI: 10.1007/BF01175043
author: Takao Yamaguchi
published in: Mathematische Zeitschrift
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173575
review text: Let M be a complete Riemannian manifold with finite volume, sectional curvature \(-\Lambda^ 2\leq K\leq 0\) and negative definite Ricci tensor at some point. Then the isometry group I(M) of M is finite; see \textit{G. Avérous} and \textit{S. Kobayashi} [Differ. Geom. Relativ., Vol. Honour A. Lichnerowicz 60th Birthday, 19-26 (1976; Zbl 0366.53025)]. Assume that M' is a bounded open submanifold of M with finite diameter d(M') which is a deformation retract of M. Then the order of I(M) is estimated from above in terms of \(\Lambda\), d(M'), dim(M) and the infimum of the injectivity radius \(i_ M(p)\) on M'.
Mathematics Subject Classification ID: 53C20
zbMATH DE Number: 3883147
zbMATH Keywords: finite volume
zbMATH Keywords: sectional curvature
zbMATH Keywords: Ricci tensor
zbMATH Keywords: isometry group
zbMATH Keywords: injectivity radius
reviewed by: Gudlaugur Thorbergsson
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3883147