Hedgehogs and their Widths in Elliptic and Hyperbolic Planes

In this paper the notion of a hedgehog in non-Euclidean geometry is introduced. More specifically, the case of 2-dimensional spaces of constant curvature is considered and, in particular, spherical hedgehogs are defined in elliptic geometry and two different notions of hedgehogs in hyperbolic geometry are studied, namely, g-hedgehogs and h-hedgehogs, which extend, respectively, the corresponding well-known notions of g-convex and h-convex curves. The construction of these curves by support functions is discussed and some relations and properties are derived. Moreover, an extended notion of a width is provided for non-Euclidean hedgehogs.