In the point view of Lie group, the cross ratio and Schwarzian derivative in C n are defined and discussed, especially the Schwarzian derivative of holomorphic mappings on the domains in matrix space C m×n is def...In the point view of Lie group, the cross ratio and Schwarzian derivative in C n are defined and discussed, especially the Schwarzian derivative of holomorphic mappings on the domains in matrix space C m×n is defined and discussed. It is proved that it is invariant up to similarity under the group of holomorphic automorphism of the Grassmann manifold C G(m,n) . And it is also proved that the Schwarzian derivative equals zero if and only if the mapping is linearly fractional.展开更多
文摘In the point view of Lie group, the cross ratio and Schwarzian derivative in C n are defined and discussed, especially the Schwarzian derivative of holomorphic mappings on the domains in matrix space C m×n is defined and discussed. It is proved that it is invariant up to similarity under the group of holomorphic automorphism of the Grassmann manifold C G(m,n) . And it is also proved that the Schwarzian derivative equals zero if and only if the mapping is linearly fractional.
