Critical metrics on connected sums of Einstein four-manifolds

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 CP2 and the product metric on S-2 x S-2. Using these metrics in various gluing configurations, toric-invariant critical metrics are found on connected sums for a specific Rie-mannian functional, which depends on the global geometry of the factors. Furthermore, using certain quotients of S-2 x S-2 as one of the gluing factors, critical metrics on several non simply-connected manifolds are also obtained. (C) 2016 Elsevier Inc. All rights reserved.