Immersion of Kähler manifolds in the class of convex submanifolds

Resumo

It is proved that a real complete convex Kähler submanifold in Euclidean space splits as a metric product of two-dimensional surfaces of positive Gaussian curvature in Euclidean 3-space and a Euclidean subspace. A theorem of V. K. Beloshapka and S. N. Bychkov is generalized to the case of convex submanifolds of any codimension.