Einstein metrics on connected sums of $S^2\times S^3$

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.