  In this paper we study a geometric configuration of submanifolds of arbitrary
codimension in an ambient Riemannian space. We obtain relations between the
geometry of a q-codimension submanifold Mn along its boundary and the geometry
of the boundary of Mn as an hypersuface of a q-codimensional submanifold Pn in
an ambient space Mn+q. As a consequence of these geometric ralations we get
that the ellipticity of the generalized Newton transformations implies the
tranversality of Mn and Pn in Pn is totally geodesic in Mn+q.
