On complete maximal submanifolds in pseudo-hyperbolic space

TL;DR

This paper classifies all complete maximal spacelike submanifolds in pseudo-hyperbolic space and explores their implications for Teichmüller theory and Anosov representations of hyperbolic groups.

Contribution

It provides a comprehensive classification of complete maximal submanifolds in pseudo-hyperbolic space and connects this to advanced theories in geometry and group representations.

Findings

Complete classification of maximal submanifolds in $ extbf{H}^{p,q}$.

Applications to Teichmüller theory.

Insights into Anosov representations of hyperbolic groups.

Abstract

We provide a full classification of complete maximal $p$-dimensional spacelike submanifolds in the pseudo-hyperbolic space $\mathbf{H}^{p,q}$, and we study its applications to Teichm\"uller theory and to the theory of Anosov representations of hyperbolic groups in $\mathsf{PO}(p,q+1)$.