We find a remarkable family of G2 structures defined on certain
principal SO(3)-bundles P±⟶M associated with any
given oriented Riemannian 4-manifold M. Such structures are always
cocalibrated. The study starts with a recast of the Singer-Thorpe equations of
4-dimensional geometry. These are applied to the Bryant-Salamon cons\-truction
of complete G2-holonomy metrics on the vector bundle of self- or
anti-self-dual 2-forms on M. We then discover new examples of that special
holonomy on disk bundles over H4 and HC2,
respectively, the real and complex hyperbolic space. Only in the end we present
the new G2 structures on principal bundles.Comment: 20 pages; final version, to appear in Annales Academi{\ae}
Scientiarum Fennic{\ae