  Isotropic hyper-elasticity, altogether with the equilibrium equation and the
usual boundary conditions, are formulated directly on the body B, a
three-dimensional compact and orientable manifold with boundary equipped with a
mass measure. Pearson-Sewell-Beatty pressure potential is formulated in an
intrinsic geometric manner. It is shown that Poincar{\'e}'s formula extended to
infinite dimension, provides, in a straightforward manner, the optimal
(non-holonomic) constraints for such a pressure potential to exist.
