The comparison theorem for the bergman and kobayashi metrics on certain pseudoconvex domains*

Abstract

The holomorphic sectional curvatures under invariant Kahler metrics on certain pseudoconvex domains E(m, n, K) are given in the explicit forms. In the meantime, we construct an invariant Kahler metric, which is complete and not less than Bergman metric, such that its holomorphic sectional curvature is bounded above by a negative constant. Hence we obtain the comparison theorem for the Bergman and Kobayashi metrics on E(m, n, K).