Geodesic
Extremal Metrics on del Pezzo Threefolds
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Multidimensional algebraic geometry, Tome 264 (2009), pp. 37-51

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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. 
@article{TM_2009_264_a3,
     author = {I. A. Cheltsov and K. A. Shramov},
     title = {Extremal {Metrics} on del {Pezzo} {Threefolds}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {37--51},
     publisher = {mathdoc},
     volume = {264},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2009_264_a3/}
}
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I. A. Cheltsov; K. A. Shramov. Extremal Metrics on del Pezzo Threefolds. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Multidimensional algebraic geometry, Tome 264 (2009), pp. 37-51. http://geodesic.mathdoc.fr/item/TM_2009_264_a3/