Self-dual and even Poincaré-Einstein metrics in dimension four

2024/07/11 by Matthew J. Gursky, Gursky, Matthew J., Stephen E. McKeown +3
Mathematics · Physics and Astronomy · #53C25 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2407.08851

openalex publication_date 2024/07/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove rigidity and gap theorems for self-dual and even Poincaré-Einstein metrics in dimension four. As a corollary, we give an obstruction to the existence of self-dual Poincaré-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.

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