The aim of this paper is to construct infinitely many families of Einstein metrics on the connected sums of arbitrary number of copies of $S^2\times S^3$. We realize these 5-manifolds as total spaces of Seifert bundles over Del Pezzo orbifolds. A K\"ahler--Einstein metric on the Del Pezzo orbifold is then lifted to an Einstein metric using the Kobayashi--Boyer--Galicki method.
Einstein Metrics, Complex Surfaces, and Symplectic 4-Manifolds
On the nonexistence of Einstein metric on 4-manifolds
Stability of Einstein metrics and effective hyperbolization
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