Extremal Metrics on del Pezzo Threefolds

We prove the existence of Kähler–Einstein metrics on a nonsingular section of the Grassmannian $\mathrm{Gr}(2,5)\subset\mathbb P^9$ by a linear subspace of codimension 3 and on the Fermat hypersurface of degree 6 in $\mathbb P(1,1,1,2,3)$. We also show that a global log canonical threshold of the Mukai–Umemura variety is equal to 1/2.