Closed p-Elastic Curves in Spheres of L³

For every p, we study p-elastic curves in the hyperbolic plane H² and in the de Sitter $2$-space H₁². We analyze the existence of closed p-elastic curves with nonconstant curvature showing that in the hyperbolic plane H² these curves exist provided that $p>1$, while in the de Sitter $2$-space H₁² the restriction $p<0$ must be satisfied.