On the conformal transformation group of a compact Riemannian manifold with constant scalar curvature
type: Item
instance of: scholarly article
title: On the conformal transformation group of a compact Riemannian manifold with constant scalar curvature
zbMATH Open document ID: 0824.53031
author: Hiroyasu Izeki
published in: Tokyo Journal of Mathematics
publication date: 1993-01-17T00:00:00Z
review text: Extending a result of \textit{N. Ejiri} [J. Math. Soc. Japan 33, 261-266 (1981; Zbl 0473.53036)], the author proves the following theorem: Let \((M_ 1, g_ 1)\) be a compact, connected, homogeneous Riemannian \(m_ 1\)-manifold and \((M_ 2, g_ 2)\) a Riemannian \(m_ 2\)-manifold with constant scalar curvature \((m_ 1 \geq 1, m_ 2 \geq 2)\). Then on \(M = M_ 1 \times M_ 2\) exists a Riemannian metric \(g\) with constant scalar curvature, such that the conformal transformation group and the isometry group of \((M,g)\) are not equal.
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 53C21
zbMATH DE Number: 97914
zbMATH Keywords: Yamabe problem
zbMATH Keywords: constant scalar curvature
zbMATH Keywords: conformal transformation group
zbMATH Keywords: isometry group
reviewed by: Valentin Boju
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1270130255
OpenAlex ID: W2039307818
Wikidata QID: Q115219792
DOI: 10.3836/TJM/1270130255
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description: scientific article; zbMATH DE number 97914