The Schwarzian derivative in Kahler manifolds

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 Neharis criterion of univalence.