Geometry & Topology

Flexing closed hyperbolic manifolds

Daryl Cooper, Darren Long, and Morwen Thistlethwaite

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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.

Article information

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M50: Geometric structures on low-dimensional manifolds

real projective structure complex isometry flexing


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.

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