In complex geometry, a Hopf manifold is obtainedas a quotient of the complex vector space(with zero deleted) by a free action of the group ofintegers, with the generator of acting by holomorphic contractions. Here, a holomorphic contractionis a map such that a sufficiently big iteration maps any given compact subset of onto an arbitrarily small neighbourhood of 0. Two-dimensional Hopf manifolds are called Hopf surfaces.