  We consider closed and orientable immersed hypersurfaces of translational
manifolds. Given a vector field on such a hypersurface, we define a
perturbation of its Gauss map, which allows us to obtain topological invariants
for the immersion that depends on the geometry of the manifold and the ambient
space. We use these quantities to find obstructions to the existence of certain
codimension one foliations.
