Geodesic transformations in almost Hermitian geometry

Abstract

We treat partially conformal geodesic transformations with respect to submanifolds in almost Hermitian manifolds. Non-isometric ones only exist when the submanifold is a real hypersurface or reduces to a point. In these two cases, we derive necessary and sufficient conditions for the existence in terms of the Jacobi operator and show how this existence influences the geometry of the hypersurface and that of the ambient space. As an application, we use these transformations to obtain a new characterization of complex space forms.