On projective transformations of complete Riemannian manifolds with constant scalar curvature
type: Item
instance of: scholarly article
zbMATH Open document ID: 0990.53027
author: Shigeyoshi Fujimura
publication date: 2002-08-12T00:00:00Z
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 53C21
Mathematics Subject Classification ID: 53C22
Mathematics Subject Classification ID: 53C25
zbMATH DE Number: 1626287
zbMATH Keywords: Riemannian manifold
zbMATH Keywords: projective transformation
zbMATH Keywords: gravitational tensor
zbMATH Keywords: Weyl's projective curvature tensor
MaRDI profile type: Publication
title: On projective transformations of complete Riemannian manifolds with constant scalar curvature
published in: Memoirs of the Institute of Science and Engineering. Ritsumeikan University
review text: The author proves two theorems for a complete and simply connected Riemannian manifold \((M,g)\) of dimension \(n>2\) with a constant scalar curvature \(R\). If there exists a non-affine projective transformation of \((M,g)\) which leaves either the gravitational tensor field (where \(R>0\)) or the covariant derivative of Weyl's projective curvature tensor invariant, then \((M,g)\) is isometric to a Euclidean sphere.
reviewed by: Josef Mikeš
description: scientific article; zbMATH DE number 1626287