Instance of a non-compact and non-euclidean complex manifolds

The only concrete example of complex manifolds neither compact nor euclidean are $\Bbb P^n(\Bbb C)\setminus K$ where $K\subset\Bbb P^n(\Bbb C)$ is compact, for $n\ge2$.

Are there other concrete examples?

Here are two classes of examples:

1. Let $X$ be a non-empty, non-Euclidean complex manifold and $Y$ a non-empty, non-compact complex manifold. Then, $X\times Y$ is a complex manifold, which is non-compact (since $Y$ is a continuous image of $X\times Y$ and non-compact) and non-Euclidean (since $X$ is non-Euclidean and a complex submanifold of $X\times Y$).

2. Let $X$ be a non-empty, compact, complex manifold and $Y\subseteq X$ be a non-empty, closed, complex submanifold of codimension $\ge2$. Then, $X\setminus Y$ is an open subset of $X$, hence a complex manifold. If $X\setminus Y$ were compact, it would be closed in $X$, since $X$ is hausdorff, so $Y$ would then be open in $X$, contradicting that $Y$ has positive codimension. Thus, $X\setminus Y$ is non-compact. Furthermore, $\dim(X\setminus Y)=\dim(X)=\dim(Y)+2\ge2$, so $X\setminus Y$ contains two distinct points. If $X\setminus Y$ embedded in some $\mathbb{C}^n$, there would be a holomorphic function $\mathbb{C}^n\rightarrow\mathbb{C}$ separating the images of these two points (e.g. a linear function would do). However, pulling this back along the embedding would yield a non-constant holomorphic function on $X\setminus Y$. Since $Y$ has codimension $\ge2$, this extends to a holomorphic function on $X$ by a Hartogs's theorem, which is constant by Liouville's theorem, contradiction. Thus, $X\setminus Y$ is non-Euclidean.