  The mathematics of a 4-dimensional renormalizable generally covariant
lagrangian model (with first order derivatives) is reviewed. The lorentzian CR
manifolds are totally real submanifolds of 4(complex)-dimensional complex
manifolds determined by four special conditions. The defining tetrad permits
the definition of a class of lorentzian metrics which admit two geodetic and
shear free congruences. These metrics permit the classification of the
structures using the Weyl tensor and the Flaherty pseudo-complex structure. The
Cartan procedure permits the definition of three relative invariants. Viewed as
a pair of two hypersurface-type 3-dimensional CR structures, the lorentzian CR
structures may be osculated on the basis of SU(1,2) group. An osculation on the
basis of SU(2,2) group reveals the Poincare group which may be identified with
the observed group in nature. Examples of static axially symmetric lorentzian
CR structures are computed. For every lorentzian CR manifold, a class of
Kaehler metrics of the ambient complex manifold is found, which induce the
class of compatible lorentzian metrics on the submanifold. Then the lorentzian
CR manifold becomes a lagrangian submanifold in the corresponding ambient
(Kaehler) symplectic manifold. The lorentzian CR manifolds may be considered as
dynamical processes in the context of the Einstein-Infeld-Hofman derivation of
the equations of motion.
