On the geometry of lambda-symmetries and PDE reduction

We give a geometrical characterization of lambda-prolongations of vector fields, and hence of lambda-symmetries of ODEs. This allows an extension to the case of PDEs and systems of PDEs; in this context the central object is a horizontal I-form mu, and we speak of mu-prolongations of vector fields and mu-symmetries of PDEs. We show that these are as good as standard symmetries in providing symmetry reduction of PDEs and systems, and explicit invariant solutions.