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 M n along its boundary and the geometry of the boundary Σ n−1 of M n as an hypersuface of a q-codimensional submanifold P n in an ambient space M n+q . As a consequence of these geometric ralations we get that the ellipticity of the generalized Newton transformations implies the tranversality of M n and P n in P n is totally geodesic in M n+q .

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