Let $H$ be a bounded symmetric domain.


What is the difference between the Bergman metric and the Kahler-Einstein metric on $H$?



Difference between Kahler-Einstein and Bergman metric on a bounded symmetric domain
The Bergman metric on any bounded symmetric domain is equal to the biholomorphism invariant Kaehler-Einstein metric, which makes it a Hermitian symmetric space. See Mok, **Metric Rigidity Theorems on Hermitian Locally Symmetric Manifolds**, p. 59, proposition 3.


