Geometry & Topology
- Geom. Topol.
- Volume 17, Number 1 (2013), 329-367.
The deformation theory of hyperbolic cone–$3$–manifolds with cone-angles less than $2\pi$
We develop the deformation theory of hyperbolic cone–3–manifolds with cone-angles less than , that is, contained in the interval . In the present paper we focus on deformations keeping the topological type of the cone-manifold fixed. We prove local rigidity for such structures. This gives a positive answer to a question of A Casson.
Geom. Topol., Volume 17, Number 1 (2013), 329-367.
Received: 12 April 2012
Accepted: 9 September 2012
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.)
Secondary: 57M50: Geometric structures on low-dimensional manifolds
Weiß, Hartmut. The deformation theory of hyperbolic cone–$3$–manifolds with cone-angles less than $2\pi$. Geom. Topol. 17 (2013), no. 1, 329--367. doi:10.2140/gt.2013.17.329. https://projecteuclid.org/euclid.gt/1513732526