Let $ \mathcal{I}^3\subset\mathbb{R}^4$ be the hyperboloid model for hyperbolic $ 3$ -space, and let $ \gamma$ be an orientation-preserving isometry of the space. Then there is a unique geodesic $ g\subset\mathcal{I}^3$ that is fixed by the action of $ \gamma$ . In general $ \gamma$ will translate along and rotate around this geodesic. For theRead more