The intrinsic metrics on the circular domains in \({\mathbb{C}}^ n\) (Q791002)

In this paper the intrinsic metrics on the circular domains in \({\mathbb{C}}^ n\) are studied. Using the results of \textit{A. Sadullaev} [Math. Notes 27, 120-125 (1980); translation from Mat. Zametki 27, 245- 253 (1980; Zbl 0431.32018)], the author calculates the Kobayashi metric at the center of a pseudoconvex complete (bounded) circular domain D. Moreover, if D is convex then the Caratheodory and Kobayashi metric coincide at the center of D. \textit{T. J. Barth} [Proc. Am. Math. Soc. 88, 527-530 (1983; Zbl 0494.32008)] has obtained the same results by a different method. In the final section the author explicitly gives the intrinsic metrics for Cartan's classical domains. For this, see the author, Math. Rep., Toyama Univ. 6, 143-177 (1983; Zbl 0522.32020).