  We consider a sequence of quantum states, $\rho_N$, associated with a
submanifold $\Lambda$ of product of two integral compact K\"ahler manifolds. We
show that, when $\Lambda$ is a product submanifold, then, in the semiclassical
limit, these states are not entangled. We discuss whether geometry of $\Lambda$
(specifically $\Lambda$ being a product submanifold) has any relationship with
entanglement properties of $\rho_N$.
