Introduces a statistical model on complex domains via probability measures, derives a covariance-based curvature formula for the Bergman metric, proves a biholomorphism criterion from metric preservation, and establishes consistency plus CLT for the Fréchet mean of Calabi's diastasis.
Seo, Weakly 1-completeness of holomorphic fiber bundles over com pact K¨ ahler manifolds, Jour- nal of the London Mathematical Society 106 (2022), no
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Statistical Bergman geometry
Introduces a statistical model on complex domains via probability measures, derives a covariance-based curvature formula for the Bergman metric, proves a biholomorphism criterion from metric preservation, and establishes consistency plus CLT for the Fréchet mean of Calabi's diastasis.