Geometry & Topology

Quakebend deformations in complex hyperbolic quasi-Fuchsian space

Ioannis D Platis

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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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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]

complex hyperbolic bending


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.

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