  A variational framework is introduced to describe how a surface bends when it
is subject to local constraints on its geometry. This framework is applied to
describe the patterns of a folded sheet of paper. The unstretchability of paper
implies a constraint on the surface metric; bending is penalized by an energy
quadratic in mean curvature. The local Lagrange multipliers enforcing the
constraint are identified with a conserved tangential stress that couples to
the extrinsic curvature of the sheet. The framework is illustrated by examining
the deformation of a flat sheet into a generalized cone.
