K\"ahler submanifolds of the symmetrized polydisc

TL;DR

This paper establishes that there are no shared Kähler submanifolds between complex Euclidean space and the symmetrized polydisc when equipped with their standard metrics, highlighting fundamental geometric incompatibilities.

Contribution

It proves the non-existence of common Kähler submanifolds between Euclidean space and the symmetrized polydisc with their canonical metrics, a new result in complex geometry.

Findings

No common Kähler submanifolds exist between the Euclidean space and the symmetrized polydisc.

The result clarifies geometric distinctions between these complex domains.

It advances understanding of metric and submanifold structures in complex analysis.

Abstract

This paper proves the non-existence of common K\"ahler submanifolds of the complex Euclidean space and the symmetrized polydisc endowed with their canonical metrics.