  The invariant projections of the energy-momentum tensors of Lagrangian
densities for tensor fields over differentiable manifolds with contravariant
and covariant affine connections and metrics [$(\bar{L}_n,g)$-spaces] are found
by the use of an non-null (non-isotropic) contravariant vector field and its
corresponding projective metrics. The notions of rest mass density, momentum
density, energy current density and stress tensor are introduced as
generalizations of these notions from the relativistic continuum media
mechanics. The energy-momentum tensors are represented by means of the
introduced notions and the corresponding identities are found. The notion of
covariant differential operator along a contravariant tensor field is
introduced. On its basis, as a special case, the notion of contravariant metric
differential operator is proposed. The properties of the operators are
considered. By the use of these operators the notion of covariant divergency of
a mixed tensor field is determined. The covariant divergency of tensor fields
of second rank of the types 1 and 2 is found. Invariant representations of the
covariant divergency of the energy-momentum tensor are obtained by means of the
projective metrics of a contravariant non-isotropic (non-null) vector field and
the corresponding rest mass density, momentum density, and energy flux density.
An invariant representation of the first Noether identity is found as well as
relations between the covariant divergencies of the different energy-momentum
tensors and their structures determining covariant local conserved quantities.
