The affine group of a compact Riemannian manifold
type: Item
instance of: scholarly article
title: The affine group of a compact Riemannian manifold
zbMATH Open document ID: 0912.53025
author: Abdelghani Zeghib
published in: Communications in Analysis and Geometry
publication date: 1997-10-26T00:00:00Z
review text: Let \(M\) be a compact Riemannian manifold. The isometry group \(\text{Isom}(M)\) of \(M\) becomes naturally a compact Lie group. The author investigates the problem whether there is a geometric structure which is weaker than the metric structure for which the group of transformations of \(M\) preserving this structure becomes a noncompact Lie group. In fact, the author considers the connection of Levi-Civita induced by the Riemannian metric and shows that if there is a noncompact group action preserving this connection, then the manifold is restricted to fairly special types of compact manifolds.
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 57S20
zbMATH DE Number: 1060140
zbMATH Keywords: noncompact group of affine transformations
zbMATH Keywords: compact Riemannian manifold
reviewed by: Akihiko Morimoto
MaRDI profile type: Publication
DOI: 10.4310/CAG.1997.V5.N1.A4
description: scientific article; zbMATH DE number 1060140