  The elastic energy functional of a thin elastic rod or sheet is generalized
to the case of an M-dimensional manifold in N-dimensional space. We derive
potentials for the stress field and curvatures and find the generalized von
Karman equations for a manifold in elastic equilibrium. We perform a scaling
analysis of an M-1 dimensional ridge in an M = N-1 dimensional manifold. A
ridge of linear size X in a manifold with thickness h << X has a width w ~
h^{1/3}X^{2/3} and a total energy E ~ h^{M} (X/h)^{M-5/3}. We also prove that
the total bending energy of the ridge is exactly five times the total
stretching energy. These results match those of A. Lobkovsky [Phys. Rev. E 53,
3750 (1996)] for the case of a bent plate in three dimensions.
