 Hopf manifold

In complex geometry, a Hopf manifold is obtained
as a quotient of the complex vector space
(with zero deleted) formula_1
by a free action of the group formula_2 of
integers, with the generator formula_3 
of formula_4 acting by holomorphic contractions.Here, a "holomorphic contraction"
is a map formula_5
such that a sufficiently big iteration formula_6
maps any given compact subset of formula_7
onto an arbitrarily small neighbourhood of 0.