Hopf manifold

In complex geometry, a Hopf manifold (Hopf 1948) is obtained as a quotient of the complex vector space (with zero deleted) ${\displaystyle ({\mathbb {C}}^{n}\backslash 0)}$ by a free action of the group ${\displaystyle \Gamma \cong {\mathbb {Z}}}$ of integers, with the generator ${\displaystyle \gamma }$ of ${\displaystyle \Gamma }$ acting by holomorphic contractions. Here, a holomorphic contraction is a map ${\displaystyle \gamma :\;{\mathbb {C}}^{n}\mapsto {\mathbb {C}}^{n}}$ such that a sufficiently big iteration ${\displaystyle \;\gamma ^{N}}$ puts any given compact subset ${\displaystyle {\mathbb {C}}^{n}}$ onto an arbitrarily small neighbourhood of 0.

...
Wikipedia