Geometry & Topology

Quakebend deformations in complex hyperbolic quasi-Fuchsian space

Ioannis D Platis

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Abstract

We study quakebend deformations in complex hyperbolic quasi-Fuchsian space Q(Σ) of a closed surface Σ of genus g>1, that is the space of discrete, faithful, totally loxodromic and geometrically finite representations of the fundamental group of Σ into the group of isometries of complex hyperbolic space. Emanating from an –Fuchsian point ρQ(Σ), we construct curves associated to complex hyperbolic quakebending of ρ and we prove that we may always find an open neighborhood U(ρ) of ρ in Q(Σ) 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.

Article information

Source
Geom. Topol., Volume 12, Number 1 (2008), 431-459.

Dates
Received: 23 February 2007
Accepted: 6 December 2007
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513800024

Digital Object Identifier
doi:10.2140/gt.2008.12.431

Mathematical Reviews number (MathSciNet)
MR2390350

Zentralblatt MATH identifier
1153.30038

Subjects
Primary: 32G05: Deformations of complex structures [See also 13D10, 16S80, 58H10, 58H15]
Secondary: 32M05: Complex Lie groups, automorphism groups acting on complex spaces [See also 22E10]

Keywords
complex hyperbolic bending

Citation

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


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