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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70109The 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 Kähler--Einstein metric on the Del Pezzo orbifold is then lifted to an Einstein metric using the Kobayashi--Boyer--Galicki method.Differential GeometryAlgebraic Geometry53C25 (primary) 32Q20, 14J26 (secondary)Einstein metrics on connected sums of $S^2\times S^3$text