On the curvature of circles and curves in \(\mathbb{H}^n\)
The author computes the curvature of smooth curves in the Poincaré-model of the hyperbolic space \(\mathbb{H}^n_a\) (with constant curvature \(-a^2)\), and applies it to arcs of Euclidean circles in \(\mathbb{H}^n_ a\). Osculating circles are used to prove that any closed curve in \(\mathbb{H}^n_a\) carries at least one point, where the curvature is greater than \(a\).
scientific article; zbMATH DE number 1619035