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.
@article{bwmeta1.element.doi-10_1515_coma-2017-0001,
author = {Michela Zedda},
title = {Strongly not relatives K\"ahler manifolds},
journal = {Complex Manifolds},
volume = {4},
year = {2017},
pages = {1-6},
zbl = {06695096},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_coma-2017-0001}
}
Michela Zedda. Strongly not relatives Kähler manifolds. Complex Manifolds, Tome 4 (2017) pp. 1-6. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_coma-2017-0001/