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2000 Mathematics Subject Classification: 53C42, 53C55.
Let M f → CP^n be an algebraic manifold of complex dimension d and let σf
be its second fundamental form. In this paper we address the following conjecture,
which is the analogue of the one stated by M. Gromov for smooth immersions: ...
We prove the conjecture in the following three cases:
(i) d = 1; (ii) M is a complete intersection; (iii) the scalar curvature of M is constant.
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...
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