New Sasaki–Einstein 5‐manifolds

Abstract

By estimating the delta$\delta$-invariants of certain log del Pezzo surfaces, we prove that closed simply connected 5-manifolds 2(S2xS3)#nM2$2(S<^>2\times S<^>3)\# nM_2$ allow Sasaki-Einstein structures, where M2$M_2$ is the closed simply connected 5-manifold with H2(M2,Z)=Z/2Z circle plus Z/2Z$\mathrm{H}_2(M_2,\mathbb {Z})=\mathbb {Z}/2\mathbb {Z}\oplus \mathbb {Z}/2\mathbb {Z}$, nM2$nM_2$ is the n$n$-fold connected sum of M2$M_2$, and 2(S2xS3)$2(S<^>2\times S<^>3)$ is the twofold connected sum of S2xS3$S<^>2\times S<^>3$.