  A locally conformally Kahler (LCK) manifold is a manifold which is covered by
a Kahler manifold, with the deck transform group acting by homotheties. We show
that the blow-up of a compact LCK manifold along a complex submanifold admits
an LCK structure if and only if this submanifold is globally conformally
Kahler. We also prove that a twistor space (of a compact 4-manifold, a
quaternion-Kahler manifold or a Riemannian m anifold) cannot admit an LCK
metric, unless it is Kahler.
