Kähler–Einstein submanifolds of the infinite dimensional projective space

This paper consists of two main results. In the first one we describe all Kähler immersions of a bounded symmetric domain into the infinite dimensional complex projective space in terms of the Wallach set of the domain. In the second one we exhibit an example of complete and non-homogeneous Kähler-Einstein metric with negative scalar curvature which admits a Kähler immersion into the infinite dimensional complex projective space.