Self-dual and even Poincar\'e-Einstein metrics in dimension four
Differential Geometry
2024-07-15 v1
Abstract
We prove rigidity and gap theorems for self-dual and even Poincar\'e-Einstein metrics in dimension four. As a corollary, we give an obstruction to the existence of self-dual Poincar\'e-Einstein metrics in terms of conformal invariants of the boundary and the topology of the bulk. As a by-product of our proof we identify a new scalar conformal invariant of three-dimensional Riemannian manifolds.
Cite
@article{arxiv.2407.08851,
title = {Self-dual and even Poincar\'e-Einstein metrics in dimension four},
author = {Matthew J. Gursky and Stephen E. McKeown and Aaron J. Tyrrell},
journal= {arXiv preprint arXiv:2407.08851},
year = {2024}
}