We present a generalization of the concept of hedgehogs to two-dimensional manifolds 
with constant curvature. The construction of these curves using support functions 
is examined, and several related properties and identities are derived. Additionally, 
an extended definition of width is introduced for non-Euclidean hedgehogs. The talk 
is based on:
Y. Martinez-Maure, D. Rochera: Hedgehogs and their Widths in Elliptic and Hyperbolic 
Planes,  The Journal of Geometric Analysis, Volume 35, article number 47 (2025).