Resumen de Real Kaehler submanifolds in codimension up to four

Sergio Chion Aguirre, Marcos Dajczer

• Let f:M2n→R2n+4 be an isometric immersion of a Kaehler manifold of complex dimension n≥5 into Euclidean space with complex rank at least 5 everywhere. Our main result is that, along each connected component of an open dense subset of M2n, either f is holomorphic in R2n+4≅Cn+2, or it is in a unique way a composition f=F∘h of isometric immersions. In the latter case, we have that h:M2n→N2n+2 is holomorphic and F:N2n+2→R2n+4 belongs to the class, by now quite well understood, of non-holomorphic Kaehler submanifolds in codimension two. Moreover, the submanifold F is minimal if and only if f is minimal.