Proves that local Kählerness of the Carathéodory metric near the boundary on strictly pseudoconvex domains implies biholomorphism to the ball, plus rigidity for constant-curvature Bergman metrics.
Lempert, Intrinsic metrics , Complex analysis of several variables (Madison, Wis., 198 2), 147– 150, Proc
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Local Rigidity of the Bergman Metric and of the K\"ahler Carath\'eodory Metric
Proves that local Kählerness of the Carathéodory metric near the boundary on strictly pseudoconvex domains implies biholomorphism to the ball, plus rigidity for constant-curvature Bergman metrics.