THE KHLER GEOMETRY ON THE REINHARDT DOMAINS

Let D = D(K) = {z = (z, z, …, z) = (z, Z) ∈ C~n| |z|+ |z|~2 < 1, K > 0, K ≠ 1}. The author has proved that the Khler metric, which is generated by the K(z, ) = (1 — | Z|~2)~(-n+(n-j)/K)[(1 — |Z|~2)- |z|~2]~(-(n+1)+j)(0 ≤ j ≤ n), is invariant on D under the Aut (D) ——the full group of the analytic automorphisms of D. Now,