Non-linear Hopf Manifolds are Locally Conformally Kähler

A Hopf manifold is a quotient of $C^n\backslash 0$ by the cyclic group generated holomorphic contraction. manifolds are diffeomorphic to $S^1\times S^{2n-1}$ and hence do not admit Kahler metrics. It known that defined linear contractions (called manifolds) have locally conformally (LCK) In this paper we prove non-linear embeddings into manifolds, and, moreover they LCK