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arXiv · 1303.0827

Critical metrics on connected sums of Einstein four-manifolds

Matthew J. Gursky·Jeff A. Viaclovsky
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Abstract

We develop a gluing procedure designed to obtain canonical metrics on connected sums of Einstein four-manifolds. The main application is an existence result, using two well-known Einstein manifolds as building blocks: the Fubini-Study metric on $\mathbb{CP}^2$ and the product metric on $S^2 \times S^2$. Using these metrics in various gluing configurations, critical metrics are found on connected sums for a specific Riemannian functional, which depends on the global geometry of the factors. Furthermore, using certain quotients of $S^2 \times S^2$ as one of the gluing factors, critical metrics on several non-simply-connected manifolds are also obtained.

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Matthew J. Gursky, Jeff A. Viaclovsky. 2013-03-04. Critical metrics on connected sums of Einstein four-manifolds. https://arxiv.org/abs/1303.0827

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