The notion of geometrical duality is discussed in the context of both Brans
-Dicke theory and general relativity. It is shown that, in some particular
solutions, the spacetime singularities that arise in usual Riemannian gener
al relativity may be avoided in its dual representation (Weyl-type general
relativity). This dual representation provides a singularity-fret picture o
f the world that is physically equivalent to the canonical general relativi
stic one.