Locally conformally flat Lorentzian quasi-Einstein manifolds

TL;DR

This paper classifies locally conformally flat Lorentzian quasi-Einstein manifolds, showing they are either globally conformally equivalent to space forms or locally isometric to specific geometric structures like $pp$-waves or warped products.

Contribution

It provides a comprehensive classification of these manifolds, connecting their local and global geometric properties in Lorentzian geometry.

Findings

They are globally conformally equivalent to space forms.

They are locally isometric to $pp$-waves or warped products.

The classification links local geometric structures to global conformal properties.

Abstract

We show that locally conformally flat quasi-Einstein manifolds are globally conformally equivalent to a space form or locally isometric to a $pp$-wave or a warped product.