Closed-form expression for the irregular dP2 Sasaki–Einstein metric

Derive a closed-form expression for the Sasaki–Einstein metric on the link of the dP2 cone at its irregular volume-minimizing Reeb vector.

Background

The paper numerically constructs the Sasaki–Einstein metric on the link of the dP2 cone at the irregular volume-minimizing Reeb vector. Unlike the previously studied Y{p,q} examples, this cone is not a member of the L{a,b,c} family, and the authors report that no closed-form metric is available for it. Consequently, the numerical construction lacks an independent closed-form reference against which the metric can be directly compared.

References

No closed form is known for it, the cone is not a member of $L{a,b,c}$, and DHHKW deferred it, so unlike every earlier target there is nothing external to check an answer against.

— Numerical Sasaki--Einstein metrics and harmonic forms on del Pezzo links  (2609.25857 - Kim et al., 22 Sep 2026) in Section 6.2, “The Sasaki–Einstein metric at b*”