Jp. Berthias et B. Shahidsaless, TORSION AND NON-METRICITY IN SCALAR TENSOR THEORIES OF GRAVITY, Classical and quantum gravity, 10(5), 1993, pp. 1039-1044
We show that the gravitational field equations derived from an action
composed of (i) an arbitrary function of the scalar curvature and othe
r scalar fields plus (ii) connection-independent kinetic and source te
rms, are identical whether one chooses non-metricity to vanish and hav
e non-zero torsion or vice versa.