The irreducibility of an affine homogeneous convex domain (Q799949)

Let \(\Omega\) be an irreducible affine homogeneous convex domain equipped with the canonical Riemannian metric. In the paper, the following theorems are proved. If \(\Omega\) is not a cone, then it is irreducible as a Riemannian manifold. The tube domain over \(\Omega\) is always irreducible as a Riemannian manifold with respect to the Bergman metric. The canonical metric of \(\Omega\) is Einstein if and only if \(\Omega\) is an ''elementary'' domain \(x_ 0>x^ 2_ 1+...+x^ 2_ n\).