2011/08/31 by Liviu Ornea, Misha Verbitsky, Victor Vuletescu · 1 citation
Mathematics · #math.AG #math.CV #math.DG #msc:53C55
published as Int. Math. Res. Not. IMRN 2013, no. 12, 2809-2821 · 14 pages, ver. 2.0, a couple of lemmas added, some amendmends for dimension 1 subvarieties
arxiv created 2011/11/15 · arxiv updated 2013/10/07
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.