  In the present paper a global conformal invariant $Y$ of a closed initial
data set is constructed. A spacelike hypersurface $\Sigma$ in a Lorentzian
spacetime naturally inherits from the spacetime metric a differentiation ${\cal
D}_e$, the so-called real Sen connection, which turns out to be determined
completely by the initial data $h_{ab}$ and $\chi_{ab}$ induced on $\Sigma$,
and coincides, in the case of vanishing second fundamental form $\chi_{ab}$,
with the Levi-Civita covariant derivation $D_e$ of the induced metric $h_{ab}$.
$Y$ is built from the real Sen connection ${\cal D}_e$ in the similar way as
the standard Chern-Simons invariant is built from $D_e$. The number $Y$ is
invariant with respect to changes of $h_{ab}$ and $\chi_{ab}$ corresponding to
conformal rescalings of the spacetime metric. In contrast the quantity $Y$
built from the complex Ashtekar connection is not invariant in this sense. The
critical points of our $Y$ are precisely the initial data sets which are
locally imbeddable into conformal Minkowski space.
