Local rigidity of hyperbolic manifolds with geodesic boundary

TL;DR

This paper proves that for compact hyperbolic n-manifolds with geodesic boundary, the holonomy representation is infinitesimally rigid when n>3, indicating a strong form of geometric stability.

Contribution

It establishes the infinitesimal rigidity of the holonomy representation for hyperbolic manifolds with boundary in dimensions greater than three, extending rigidity results.

Findings

Holonomy representation is infinitesimally rigid for n>3

Rigidity holds for manifolds with totally geodesic boundary

Extends classical rigidity results to manifolds with boundary

Abstract

Let W be a compact hyperbolic n-manifold with totally geodesic boundary. We prove that if n>3 then the holonomy representation of pi_1 (W) into the isometry group of hyperbolic n-space is infinitesimally rigid.