  In this paper, a class of holomorphic invariant metrics is introduced on the
irreducible classical domains of type I-IV, which are strongly pseudoconvex
complex Finsler metrics in the strict sense of M. Abate and G. Patrizio[2].
These metrics are of particular interest in several complex variables since
they are holomorphic invariant complex Finsler metrics found so far in
literature which enjoy good regularity as well as strong pseudoconvexity and
can be explicitly expressed so as to admit differential geometric studies. They
are, however, not necessarily Hermitian quadratic as that of the Bergman
metrics. These metrics are explicitly constructed via deformation of the
corresponding Bergman metric on the irreducible classical domains of type I-IV,
respectively, and they are all proved to be complete Kahler-Berwald metrics.
They enjoy very similar curvature properties as that of the Bergman metric on
the irreducible classical domains, namely their holomorphic sectional
curvatures are bounded between two negative constants, and their holomorphic
bisectional curvatures are always non positive and bounded below by negative
constants, respectively. From the viewpoint of complex analysis, these metrics
are analogues of Bergman metrics in complex Finsler geometry which do not
necessarily have Hermitian quadratic restrictions in the viewpoint of S.-S.
Chern[7].
