A brief note on the limit omega ->infinity in Weyl geometrical scalar-tensor theory

We obtain vacuum solutions in the presence of a cosmological constant in the context of the Weyl geometrical scalar-tensor theory. We investigate the limit when omega goes to infinity and show by working out the solutions that in this limit there are some cases in which the scalar field tends to a constant (with the implicit consequence of the geometry becoming Riemannian), although the solutions do not reduce to the corresponding Einstein solutions. We have also extended a previous result, known in the literature, by showing that in the case of vacuum with cosmological constant the field equations of the Weyl geometrical scalar-tensor theory are formally identical to Brans-Dicke field equations, even though these theories are not physically equivalent.