  We study conditions on a generic connection written in terms of first-order
derivatives of the vielbein in order to obtain (possible) equivalent theories
to Einstein Gravity. We derive the equations of motion for these theories which
are based on the new connections. We recover the Teleparallel Gravity equations
of motion as a particular case. The analysis of this work might be useful to
Double Field Theory to find other connections determined in terms of the
physical fields.
