Strongly not relatives Kaehler manifolds

TL;DR

This paper investigates Kaehler manifolds that are strongly not relative to any projective Kaehler manifold, establishing their properties and relation to full Kaehler immersions, with applications to specific domain families.

Contribution

It introduces the concept of strongly not relative Kaehler manifolds and links this property to full Kaehler immersions into infinite-dimensional projective space.

Findings

Certain Kaehler manifolds are strongly not relative to projective Kaehler manifolds.

Full Kaehler immersions relate to the strongly not relative property.

Specific domain families are shown to be strongly not relative.

Abstract

In this paper we study Kaehler manifolds that are strongly not relative to any projective Kaehler manifold, i.e. those Kaehler manifolds that do not share a Kaehler submanifold with any projective Kaehler manifold even when their metric is rescaled by the multiplication by a positive constant. We prove two results which highlight some relations between this property and the existence of a full Kaehler immersion into the infinite dimensional complex projective space. As application we get that the 1-parameter families of Bergman-Hartogs and Fock-Bargmann-Hartogs domains are strongly not relative to projective Kaehler manifolds.