摘要
Let f be a holomorphic immersion which maps a Kahler manifold into a Kahler manifold of the same dimension. A Schwarzian derivative Sf of f is proposed. It is proved that: i) if Sf=0 and Sg=0, then Sf·g=0; ii) if the ’real part of the Schwarzian derivative of f on a convex domain in the Kaler manifold is bounded above, then F is an embedding. The upper bound is related to the holomorphic sectional curvature of the domain. This second theorem is an extension of Nehari’s criterion of univalence.
Let f be a holomorphic immersion which maps a Kahler manifold into a Kahler manifold of the same dimension. A Schwarzian derivative Sf of f is proposed. It is proved that: i) if Sf=0 and Sg=0, then Sf·g=0; ii) if the 'real part of the Schwarzian derivative of f on a convex domain in the Kaler manifold is bounded above, then F is an embedding. The upper bound is related to the holomorphic sectional curvature of the domain. This second theorem is an extension of Nehari's criterion of univalence.
基金
the National Natural Science Foundation of China
