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

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.