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Definition: A Hermitian symmetric domain is a Hermitian manifold that is connected, homogeneous, has a symmetry at some point (by homogenity hence every point), and has negative curvature. I want to ...

Let $(M,g)$ be an Hermitian locally symmetric space with nonnegative bisectional curvature. Suppose the fundamental group of $M$ is finite, can we prove that $M$ is simply-connected?

Let $G$ be a bounded homogeneous domain in $\mathbb{C}^{n}$ and let $z\in G$. Assume that $f$ is a holomorphic function on $G$, which is isotropy symmetric, i.e. $f\circ \varphi=f$ for any ...

Let $G$ be a domain in $\mathbb{C}^{n}$ and let $Aut(G)$ be the group of biholomorphic selfmaps of $G$. $G$ is called: (1) homogeneous if $Aut(G)$ acts transitively on $G$, i.e. for any $z,w\in G$ ...