ABSTRACT

The purpose of this chapter is to prove a Berger type normal holonomy theorem for complex submanifolds of CPn. This is done by lifting such submanifolds to Cn+1

and applying Euclidean submanifold geometry. The techniques used in this chapter combine most of the techniques developed in previous chapters. So, besides the intrinsic importance of this topic, we believe that it also has a valuable didactic interest. This section is based on the article [93] (and we also correct some minor errors in it).