THE SCHWARZIAN DERIVATIVE IN SEVERAL COMPLEX-VARIABLES (III)

In the point view of Lie group, the cross ratio and Schwarzian derivat ive in C-n are defined and discussed, especially the Schwarzian deriva tive of holomorphic mappings on the domains in matrix space C-mxn is d efined and discussed. It is proved that it is invariant up to similari ty under the group of holomorphic automorphism of the Grassmann manifo ld CG(m, n). And it is also proved that the Schwarzian derivative equa ls zero if and only if the mapping is linearly fractional.