Complex invariant Einstein metrics on $S{O}_{2(n_1+n_2+n_3)+1}/U_{n_1}\times U_{n_2}\times S{O}_{2n_3+1}$ and Ricci-flat manifolds

Alexey Lavrov

We prove that the number of complex invariant Einstein metrics on the flag manifold $M_{n_1,n_2,n_3}=S{O}_{2(n_1+n_2+n_3)+1}/U_{n_1}\times U_{n_2}\times S{O}_{2n_3+1}$ is equal to 13…