  It is shown how can be made the classification of all tensors constructed
from the Riemann tensor that verify the conservation of gravitational energy
momentum. More precisely we explain that there exists a unique tensor of degree
n in the Riemann tensor and its contractions that verifies the conservation of
energy. We show that this tensor, only because it obeys this degree n structure
as well as energy conservation, two facts which are true in all dimensions,
verifies in dimension 2n this striking particularity of being Euler gravity. We
stick here to the case n=2 but explain briefly why the general case is similar.
