Einstein deformations of hyperbolic metrics (Q2771296)

This paper discusses Einstein metrics on the hyperbolic space \(\mathbb{K}H^m\) (where \(\mathbb{K}=\mathbb{R}\), \(\mathbb{C}\), \(\mathbb{H}\) or \(\mathbb{O}\) when \(m=2\)). The main result states that all Einstein deformations of the standard symmetric metrics of \(\mathbb{K}H^m\) can be obtained as solutions to the following problem: given a Carnot-Carathéodory metric \(\gamma\) on the boundary sphere of \(\mathbb{K}H^m\), compatible in some sense with a contact structure, find a metric \(g\) in the interior satisfying the conditions: (1) \(\text{Ric}^g=-\lambda g\) and, (2) the conformal class \([\lambda]\) represents the conformal infinity of \(g\) (in LeBrun's terminology).NEWLINENEWLINEFor the entire collection see [Zbl 0961.00021].