Geometry & Topology
- Geom. Topol.
- Volume 12, Number 1 (2008), 431-459.
Quakebend deformations in complex hyperbolic quasi-Fuchsian space
We study quakebend deformations in complex hyperbolic quasi-Fuchsian space of a closed surface of genus , that is the space of discrete, faithful, totally loxodromic and geometrically finite representations of the fundamental group of into the group of isometries of complex hyperbolic space. Emanating from an –Fuchsian point , we construct curves associated to complex hyperbolic quakebending of and we prove that we may always find an open neighborhood of in containing pieces of such curves. Moreover, we present generalisations of the well known Wolpert–Kerckhoff formulae for the derivatives of geodesic length function in Teichmüller space.
Geom. Topol., Volume 12, Number 1 (2008), 431-459.
Received: 23 February 2007
Accepted: 6 December 2007
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Platis, Ioannis D. Quakebend deformations in complex hyperbolic quasi-Fuchsian space. Geom. Topol. 12 (2008), no. 1, 431--459. doi:10.2140/gt.2008.12.431. https://projecteuclid.org/euclid.gt/1513800024