On the normal holonomy representation of spacelike submanifolds in pseudo-Riemannian space forms

Abstract

In this paper we study weakly irreducible holonomy representations of the normal connection of a spacelike submanifold in a pseudo-Riemannian space from. We associate screen representations to weakly irreducible normal holonomy groups and classify the screen representations having the Borel-Lichn\'erowicz property. In particular, we derive a classification of Lorentzian normal holonomy representations.