Relative equilibria of the RTBP in curved spaces Carles Sim\'o Slides of a talk given in the conference on Global Dynamics in Hamiltonian Systems held in Nuria (Girona, Catalonia), June 28 to July 4, 2015 Abstract We want to study the relative equilibria of restricted three-body problem in the two-dimensional sphere. The curvature is used as a parameter, so that it is possible to look for solutions which can be obtained from continuation of the planar case. But there exist other solutions which cannot be obtained from the planar case. The conditions for the relative equilibria allow to look for positions of the primaries, and for collinear and triangular equilibria for the massless body, as well as some limit cases. Then the spectral stability of the equilibria is studied. The analytical results are complemented with numerical studies, both using a fine grid in suitable variables and carrying out numerical continuation from some limit solutions.