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A Note on the L2-norm of the Second Fundamental Form of Algebraic Manifolds

Loi, Andrea;  Zedda, Michela — 2010

Serdica Mathematical Journal

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.

Strongly not relatives Kähler manifolds

Michela Zedda — 2017

Complex Manifolds

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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