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

Matthew J. Gursky; Stephen E. McKeown; Aaron J. Tyrrell

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arXiv · 2407.08851

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

Matthew J. Gursky·Stephen E. McKeown·Aaron J. Tyrrell

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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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BibTeX RIS

Matthew J. Gursky, Stephen E. McKeown, Aaron J. Tyrrell. 2024-07-11. Self-dual and even Poincaré-Einstein metrics in dimension four. https://arxiv.org/abs/2407.08851

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