  We construct the family of bilinear forms gG on R3+1 for which Galilea boosts
and spatial rotations are isometries. The key feature of these bilinear forms
is that they are parametrized by a Galilea invariant vector whose physical
interpretation is rather unclear. At the end of the paper, we construct the
Poisson bracket associated to the (nondegenerate) antisymmetric part of gG.
