About pseudo-Riemannian Lichnerowicz conjecture

TL;DR

This paper constructs the first known examples of compact pseudo-Riemannian manifolds with essential conformal groups that are not conformally flat, covering all types $(p,q)$ with $2 \,\leq\, p \leq q$.

Contribution

It provides the first explicit examples of such manifolds, advancing understanding of the pseudo-Riemannian Lichnerowicz conjecture.

Findings

Examples cover all types $(p,q)$ with $2 \leq p \leq q$

Manifolds have essential conformal groups

Examples are not conformally flat

Abstract

We construct the first known examples of compact pseudo-Riemannian manifolds having an essential group of conformal transformations, and which are not conformally flat. Our examples cover all types $(p,q)$, with $2 \leq p \leq q$.