Geometry & Topology
- Geom. Topol.
- Volume 11, Number 4 (2007), 2413-2440.
Flexing closed hyperbolic manifolds
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.
Geom. Topol., Volume 11, Number 4 (2007), 2413-2440.
Received: 18 December 2006
Accepted: 3 September 2007
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 57M50: Geometric structures on low-dimensional manifolds
Cooper, Daryl; Long, Darren; Thistlethwaite, Morwen. Flexing closed hyperbolic manifolds. Geom. Topol. 11 (2007), no. 4, 2413--2440. doi:10.2140/gt.2007.11.2413. https://projecteuclid.org/euclid.gt/1513799985