  We consider the energy and bienergy functionals as variational problems on
the set of Riemannian metrics and present a study of the biharmonic
stress-energy tensor. This approach is then applied to characterise weak
conformality of the Gauss map of a submanifold. Finally, working at the level
of functionals, we recover a result of Weiner linking Willmore surfaces and
pseudo-umbilicity.
