  Consider a codimension $1$ submanifold $N^n\subset M^{n+1}$, where
$M^{n+1}\subset\mathbb{R}^{n+2}$ is a hypersurface. The envelope of tangent
spaces of $M$ along $N$ generalizes the concept of tangent developable surface
of a surface along a curve. In this paper, we study the singularities of these
envelopes.
  There are some important examples of submanifolds that admit a vector field
tangent to $M$ and transversal to $N$ whose derivative in any direction of $N$
is contained in $N$. When this is the case, one can construct transversal plane
bundles and affine metrics on $N$ with the desirable properties of being
equiaffine and apolar. Moreover, this transversal bundle coincides with the
classical notion of Transon plane. But we also give an explicit example of a
submanifold that do not admit a vector field with the above property.

Differential Geometry