Ricci Solitons on Lorentzian Manifolds with Large Isometry Groups

TL;DR

This paper classifies Lorentzian Ricci solitons with large isometry groups, showing they are expanding, steady, or shrinking, and provides examples of non-rigid, locally conformally flat, symmetric solitons.

Contribution

It characterizes Lorentzian Ricci solitons with large isometry groups and constructs explicit non-rigid examples.

Findings

Lorentzian manifolds with large isometry groups are Ricci solitons.

Examples of complete, locally conformally flat, symmetric Ricci solitons are provided.

Classification includes expanding, steady, and shrinking Ricci solitons.

Abstract

We show that Lorentzian manifolds whose isometry group is of dimension at least $\frac{1}{2}n(n-1)+1$ are expanding, steady and shrinking Ricci solitons and steady gradient Ricci solitons. This provides examples of complete locally conformally flat and symmetric Lorentzian Ricci solitons which are not rigid.