In this paper we
study the intrinsic metrics for the circular domains in Cn. We calculate the
Kobayashi (pseudo-) metric at its center for pseudoconvex complete circular
domain D using the result of Sadullaev. From this we have that such D is
hyperbolic iff D is bounded. If a convex complete circular domain is complete
hyperbolic, then the Carathéodory and Kobayashi metrics coincide at the
center. Using this and the results of Hua we explicitly compute the intrinsic
metrics of the classical domains. Furthermore we define the extremal function
and extremal disc for intrinsic metrics and compute them in some special
cases.
