Equivalence of the Khler-Einstein Metric and the Bergman Metric on Cartan-Hartogs Domain

We study the equivalence of the K(?)hler-Einstein metric and the Bergman metric on Cartan-Hartogs domain of the second type.By constructing a new complete K(?)hler metricω_(gλ)which is equivalent to the Bergman metric,we can get the Ricei curvature and the holomorphic sectional curvature with negative upper and lower bounds under this metric.Then applying Yau's Schwarz lemma we prove the K(?)hler-Einstein metric is also equivalent to the new metricω_(gλ).As a result,we obtain that the Bergman metric is equivalent to the K(?)hler-Einstein metric.