  We compute the Euclidean action for constant curvature black holes (CCBHs),
as an attempt to associate thermodynamic quantities to these solutions of
Einstein anti-de Sitter (AdS) gravity. CCBHs are gravitational configurations
obtained by identifications along isometries of a $D$-dimensional globally AdS
space, such that the Riemann tensor remains constant. Here, these solutions are
interpreted as extended objects, which contain a $(D-2)$-dimensional de-Sitter
brane as a subspace. Nevertheless, the computation of the free energy for these
solutions shows that they do not obey standard thermodynamic relations.
