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Is it true that a bounded domain $\Omega \subset \mathbb C^n$ equipped with a homogeneous metric (not necessarily a Bergman metric) has (constant) negative sectionalscalar curvature?
Is it true that a bounded domain $\Omega \subset \mathbb C^n$ equipped with a homogeneous metric (not necessarily a Bergman metric) has (constant) negative sectional curvature?
Is it true that a bounded domain $\Omega \subset \mathbb C^n$ equipped with a homogeneous metric (not necessarily a Bergman metric) has (constant) negative scalar curvature?
Is it true that a bounded domain $\Omega \subset \mathbb C^n$ equipped with a homogeneous metric (not necessarily a Bergman metric) has (constant) negative sectional curvature?
