  We consider the N=1 supersymmetric two-dimensional non-linear sigma model
with boundaries and nonzero B-field. By analysing the appropriate currents we
describe the full set of boundary conditions compatible with N=1 superconformal
symmetry. Using this result the problem of finding a correct action is
discussed. We interpret the supersymmetric boundary conditions as a maximal
integral submanifold of the target space manifold, and speculate about a new
geometrical structure, the deformation of an almost product structure.
