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

TL;DR

This paper classifies the normal holonomy representations of spacelike submanifolds in pseudo-Riemannian space forms, focusing on weakly irreducible cases and deriving a specific classification for Lorentzian representations.

Contribution

It introduces a classification framework for weakly irreducible normal holonomy groups and their screen representations, including a detailed classification of Lorentzian cases.

Findings

Classification of weakly irreducible normal holonomy groups

Introduction of screen representations with Borel-Lichnérowicz property

Specific classification of Lorentzian normal holonomy representations

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.