Does there exist any complex Lie group $G$ such that there are some positive-dimensional compact almost complex submanifolds (for example, $\mathbb{C}P^m$) of $G$?
I findwant to get some examples.
This is motivated by the following Corollary 1.21:
from Complex Manifolds,
Lecture Notes written by Clemens Koppensteiner (link)
Question: does there exist any complex Lie groups $G$ such that there are some compact almost complex submanifoldsProposition 1.20 (for example, $\mathbb{C}P^m$)Generalization of $G$? I want to get some examplesLiouville's theorem). Let $M$ be a compact [complex] manifold and $f$ a holomorphic function on $M$. Then $f$ is constant.
Corollary 1.21 There exist no compact complex submanifolds of $\mathbb{C}^n$ of positive dimension
Scan including the proofs:
