New Sasaki-Einstein 5-manifolds

TL;DR

This paper proves the existence of Sasaki-Einstein structures on certain closed, simply connected 5-manifolds, expanding the known classes of manifolds admitting such geometric structures.

Contribution

It establishes that specific connected sums of known 5-manifolds admit Sasaki-Einstein metrics, providing new examples in geometric analysis.

Findings

Sasaki-Einstein structures exist on 2(S^2×S^3) # nM_2 manifolds

Identification of new classes of 5-manifolds with Sasaki-Einstein metrics

Extension of known geometric structures to broader manifold classes

Abstract

We prove that closed simply connected $5$-manifolds $2(S^2\times S^3)\# nM_2$ allow Sasaki-Einstein structures, where $M_2$ is the closed simply connected $5$-manifold with $\mathrm{H}_2(M_2,\mathbb{Z})=\mathbb{Z}/2\mathbb{Z}\oplus \mathbb{Z}/2\mathbb{Z}$, $nM_2$ is the $n$-fold connected sum of $M_2$, and $2(S^2\times S^3)$ is the two-fold connected sum of $S^2\times S^3$.