  New Lorentz Invariance Relations (LIRs) were presented between twist-three
Generalized Parton Distributions (GPDs) and transverse momentum, $k_T$, moments
of twist-two Generalized Transverse Momentum-Dependent Distributions (GTMDs).
By implementing both these LIRs and the QCD Equations of Motion in the quark
quark correlation function, we generated a new series of Wandzura Wilczek (WW)
relations in the off-forward sector. Two of these WW relations take on a
particularly interesting physical meaning in that they provide a clear
interpretation of the QCD structure of Orbital Angular Momentum (OAM) in the
nucleon. In particular, they provide a solution to the outstanding puzzle of
how OAM could be simultaneously described by twist-two GTMDs and twist-three
GPDs. Additional relations were discussed, in particular, for the helicity
configurations that can be detected analyzing specific spin asymmetries: one
corresponding to a longitudinally polarized quark in an unpolarized proton,
associated with spin-orbit correlations, and one for transverse proton
polarization, as a generalization of the relation obeyed by the $g_2$ structure
function; finally, we defined a relation connecting the off-forward extension
of the Sivers function to an off-forward Qiu-Sterman term.
