Geometry & Topology 11 (2007) 2413–2440

DOI: 10.2140/gt.2007.11.2413

Abstract

We show that for certain closed hyperbolic manifolds, one can nontrivially deform the real hyperbolic structure when it is considered as a real projective structure. It is also shown that in the presence of a mild smoothness hypothesis, the existence of such real projective deformations is equivalent to the question of whether one can nontrivially deform the canonical representation of the real hyperbolic structure when it is considered as a group of complex hyperbolic isometries. The set of closed hyperbolic manifolds for which one can do this seems mysterious.

Keywords

real projective structure, complex isometry, flexing

Mathematical Subject Classification

Primary: 57M50

References

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Publication

Received: 18 December 2006
Accepted: 3 September 2007
Published: 17 December 2007
Proposed: Walter Neumann
Seconded: Dave Gabai, Martin Bridson

Authors