Complete locally conformally flat manifolds of negative curvature

2006/08/01 by Miguel Brozos‐Vázquez, Miguel Brozos-Vázquez, Eduardo García‐Río +3 · 30 citations
Mathematics · #Base (topology) #Computer science #Constant (computer programming) #Constant curvature #Construct (python library) #Curvature #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry #Geometry and complex manifolds #Mathematical analysis #Mathematics #Negative curvature #Product (mathematics) #Pure mathematics #Ricci-flat manifold #Scalar curvature #Sectional curvature

paper · pdf · doi:10.2140/pjm.2006.226.201

published in Pacific Journal of Mathematics 226(2), 201-219 (Mathematical Sciences Publishers)

crossref issued 2006/08/01 · crossref published 2006/08/01 · crossref published-print 2006/08/01 · openalex publication_date 2006/08/01 · crossref created 2009/10/23 · crossref deposited 2019/02/24 · openalex created_date 2025/10/10 · crossref indexed 2026/07/31 · openalex updated_date 2026/07/31

Abstract

We construct new examples of complete locally conformally flat manifolds of negative curvature by means of warped product and multiply warped product structures.Special attention is paid to those spaces with one-dimensional base, thus generalizing the Robertson-Walker spacetimes, and to those with higher-dimensional base of constant curvature.

Citations

• Conformal de Rham decomposition of Riemannian manifolds
• Twisted products in pseudo-Riemannian geometry
• Conformally flat manifolds, Kleinian groups and scalar curvature
• Manifolds of negative curvature
• Le Spectre d’une Variété Riemannienne

Cited by

• On conformally flat minimal Legendrian submanifolds in the unit sphere