  We prove the existence of Kahler-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 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.
