Recall that a Hopf manifold is a quotient $\mathbb C^n\setminus 0$ by a free action of $\mathbb Z$ where the generator is acting by a holomorphic contraction.
Question 1. Is it true that any deformation of a Hopf manifold (as a complex manifold) is again a Hopf manifold for $n\ge 3$?
Question 2. Is there some kind of classification of Hopf manifolds and their deformations in dimension $\ge 3$ (for example $n=3$).
Note that for $n=2$ the answer to both questions is positive https://en.wikipedia.org/wiki/Hopf_surface