Kaehler-Einstein submanifolds of the infinite dimensional projective space

TL;DR

This paper characterizes Kaehler immersions of bounded symmetric domains into infinite dimensional projective space and provides an example of a complete, non-homogeneous Kaehler-Einstein metric with negative scalar curvature that admits such an immersion.

Contribution

It describes all Kaehler immersions of bounded symmetric domains into infinite dimensional projective space using the Wallach set and presents a novel example of a non-homogeneous Kaehler-Einstein metric with negative scalar curvature.

Findings

All Kaehler immersions characterized via Wallach set.

Constructed example of non-homogeneous Kaehler-Einstein metric.

Established conditions for immersions of symmetric domains.

Abstract

This paper consists of two main results. In the first one we describe all Kaehler 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 Kaehler-Einstein metric with negative scalar curvature which admits a Kaehler immersion into the infinite dimensional complex projective space.