The Normal holonomy group of Kahler submanifolds

We give the list of possible holonomy groups of the normal connection of a complex submanifold of the projective space. Our approach follows the work of Carlos Olmos who proved that the normal holonomy group of a submanifold of the euclidean space acts as the isotropy representation of a symmetric space. We also prove several theorems about the geometry of the normal connection of Kahler-Einstein submanifolds. It is interesting to notice that for non-full Kahler-Einstein submanifolds the Einstein constant is related to the behaviour of the complex structure in the normal space.