Complete locally conformally flat manifolds of negative curvature

Miguel Brozos-Vázquez, Eduardo García-Río and Ramón Vázquez-Lorenzo

Vol. 226 (2006), No. 2, 201–219

DOI: 10.2140/pjm.2006.226.201

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.

Keywords

Locally conformally flat, warped product metric, Möbius equation, Obata equation

Mathematical Subject Classification 2000

Primary: 53C15, 53C50

Milestones

Received: 22 November 2004

Revised: 15 February 2005

Accepted: 15 February 2005

Published: 1 August 2006