We first extend the construction of the pressure metric to the deformation space of globally hyperbolic maximal Cauchy-compact anti-de Sitter structures. We show that, in contrast with the case of the Hitchin components, the pressure metric is degenerate and we characterize its degenerate locus. We then introduce a nowhere degenerate Riemannian metric adapting the work of Qiongling Li on the SL (3 , R) -Hitchin component to this moduli space. We prove that the Fuchsian locus is a totally geodesic copy of Teichmüller space endowed with a multiple of the Weil–Petersson metric.
Riemannian metrics on the moduli space of GHMC anti-de Sitter structures
Tamburelli A.
Primo
2020-01-01
Abstract
We first extend the construction of the pressure metric to the deformation space of globally hyperbolic maximal Cauchy-compact anti-de Sitter structures. We show that, in contrast with the case of the Hitchin components, the pressure metric is degenerate and we characterize its degenerate locus. We then introduce a nowhere degenerate Riemannian metric adapting the work of Qiongling Li on the SL (3 , R) -Hitchin component to this moduli space. We prove that the Fuchsian locus is a totally geodesic copy of Teichmüller space endowed with a multiple of the Weil–Petersson metric.File in questo prodotto:
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