Brans-Dicke-type models with nonmetricity

A scalar-tensor-nonmetric theory of gravity without matter fields is shown to be equivalent to the scalar-tensor-torsion theory proposed by German, the only difference being in the source of the Weyl vector or torsion vector (for equivalently the scalar field) which remains arbitrary in the theory. General extended conformal transformations, which leave the curvature tensor invariant, are presented and their implications for metric-affine theories and scalar-tensor theories are discussed.