  We introduce and study the notion of null manifold. This is a smooth manifold
${\mathcal N}$ endowed with a degenerate metric $\gamma$ with one-dimensional
radical at every point. We also define the notion of ruled null manifold, which
is a special case of null manifolds. We prove that ruled null manifolds are in
one-to-one correspondence with equivalence classes of null metric hypersurface
data. This correspondence is used to endow any null manifold $({\mathcal
N},\gamma)$ with a family of torsion-free connections related to each other by
a well-defined gauge group. The whole construction allows one to define and use
geometric notions on arbitrary null manifolds. The paper has a second part
where we introduce a canonical map on any null metric hypersurface data and use
its algebraic properties to define a canonical decomposition of any symmetric
(0,2)-covariant tensor. This decomposition, together with two new differential
operators compatible with this splitting, are used to decompose the constraint
tensor in full generality and at the purely abstract level. This leads to a
hierarchical structure of the (detached) Einstein vacuum null constraint
equations without the need of introducing special coordinates or special
foliations. The results are applied to study null shells arising from the
matching of two spacetimes across null boundaries. The equations governing such
objects are obtained in hierarchical form without imposing any topological,
gauge or coordinate conditions on the shell.
