Khler-Einstein surface and symmetric space

We consider the question of characterizing compact quotients of the complex 2-ball by curvature conditions, which improve the known results. Moreover, we also give curvature conditions such that a compact Khler-Einstein surface is bi-holomorphic to a locally symmetric space.

We consider the question of characterizing compact quotients of the complex 2-ball by curvature conditions, which improve the known results. Moreover, we also give curvature conditions such that a compact Kaehler-Einstein surface is bi-holomorphic to a locally symmetric space.