We consider the principal configurations associated to
smooth vector fields $\nu$ normal to a manifold $M$ immersed into a
euclidean space
and give conditions on the number of principal directions shared by a
set of
$k$ normal vector fields in order to guaranty the umbilicity of $M$
with respect
to some normal field $\nu$.
Provided that the umbilic curvature is constant, this will imply that
$M$ is
hyperspherical.
We deduce some results concerning binormal fields and asymptotic
directions
for manifolds of codimension 2. Moreover, in the case of a surface
$M$ in
$\mathbb R^N$, we conclude that if $N>4$, it is always possible to find
some
normal
field with respect to which $M$ is umbilic and provide a geometrical
characterization of such fields.