Holomorphic geodesic transformations

Abstract

We treat holomorphic geodesic transformations with respect to points and (holomorphic) submanifolds in an almost Hermitian manifold. We derive necessary and sufficient conditions for the existence and study how it influences the geometry of the submanifold. Furthermore, we use these transformations to characterize locally Hermitian symmetric spaces and complex space forms. Also, we determine all holomorphic geodesic transformations in such space forms.