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Strongly not relatives Kähler manifolds
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Abstract
In this paper we study Kähler manifolds that are strongly not relative to any projective Kähler manifold, i.e. those Kähler manifolds that do not share a Kähler submanifold with any projective Kähler 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 Kähler 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 Kähler manifolds.
Title: Strongly not relatives Kähler manifolds
Description:
Abstract
In this paper we study Kähler manifolds that are strongly not relative to any projective Kähler manifold, i.
e.
those Kähler manifolds that do not share a Kähler submanifold with any projective Kähler 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 Kähler 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 Kähler manifolds.
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