Quakebend deformations in complex hyperbolic quasi-Fuchsian space

Platis, Ioannis D¹

¹ Department of Mathematics, Aristotle University of Salonica, Salonica, Greece

Geometry & topology, Tome 12 (2008) no. 1, pp. 431-459.

Résumé

We study quakebend deformations in complex hyperbolic quasi-Fuchsian space ${\mathcal{Q}}_{ℂ}\left(\Sigma \right)$ of a closed surface $\Sigma$ of genus $g>1$, that is the space of discrete, faithful, totally loxodromic and geometrically finite representations of the fundamental group of $\Sigma$ into the group of isometries of complex hyperbolic space. Emanating from an $ℝ$–Fuchsian point $\rho \in {\mathcal{Q}}_{ℂ}\left(\Sigma \right)$, we construct curves associated to complex hyperbolic quakebending of $\rho$ and we prove that we may always find an open neighborhood $U\left(\rho \right)$ of $\rho$ in ${\mathcal{Q}}_{ℂ}\left(\Sigma \right)$ 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.

Détail

DOI : 10.2140/gt.2008.12.431

Keywords: complex hyperbolic, bending

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