Constant scalar curvatures on warped product manifolds
type: Item
instance of: scholarly article
title: Constant scalar curvatures on warped product manifolds
zbMATH Open document ID: 0893.53016
author: Paul E. Ehrlich
author: Yoon-Tae Jung
author: seon-bu Kim
published in: Tsukuba Journal of Mathematics
publication date: 1998-01-12T00:00:00Z
review text: The authors study the question when a pseudo-Riemannian metric of constant scalar curvature can be produced on a product manifold by a warped product construction. Specifically, they produce results for two different classes of pseudo-Riemannian manifolds. The first class consists of generalized Robertson-Walker spacetimes, where the base manifold \(B\) is an open interval with negative definite metric and the fiber \(F\) is a Riemannian manifold of dimension greater than 1 and with constant scalar curvature. In this case, the problem reduces to studying an associated differential equation. The second class consists of warped products, where the base \(B\) is a compact Riemannian manifold and the fiber \(F\) is a pseudo-Riemannian manifold of constant scalar curvature. In this case, the method of upper and lower solutions of partial differential equations is employed, as well as variational arguments.
Mathematics Subject Classification ID: 53C21
Mathematics Subject Classification ID: 58D30
Mathematics Subject Classification ID: 53C50
Mathematics Subject Classification ID: 58J05
zbMATH DE Number: 1102816
zbMATH Keywords: generalized Robertson-Walker spacetimes
zbMATH Keywords: constant scalar curvature
zbMATH Keywords: warped products
zbMATH Keywords: pseudo-Riemannian manifold
reviewed by: Dean E. Allison
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.21099/tkbjm/1496162996
OpenAlex ID: W1607146642
Wikidata QID: Q125762299
DOI: 10.21099/TKBJM/1496162996
description: scientific article; zbMATH DE number 1102816