Boundary conditions and gluing conditions for open strings and D-branes in the SL(2, R) WZWN model, corresponding to AdS , are discussed. Some boundary conditions and gluing conditions previously considered in the literature are shown to be incompatible with the variation principle. We then consider open string boundary conditions corresponding to a certain field-dependent gluing condition. This allows us to consider open strings with constant energy and angular momentum. Classically, these open strings naturally generalize the open strings in flat Minkowski space. For rigidly rotating open strings, we show that the torsion leads to a bending and an unfolding. We also derive the SL(2, R) Regge relation, which generalizes the linear Minkowski Regge relation. For "high" mass, it takes the form L ≈ ± M/H, where H is the scale of the SL(2, R) group manifold.