  The first purpose of this note is to comment on a recent article of Bursztyn,
Lima and Meinrenken, in which it is proved that if M is a smooth submanifold of
a manifold V, then there is a bijection between germs of tubular neighborhoods
of M and germs of "Euler-like" vector fields on V. We shall explain how to
approach this bijection through the deformation to the normal cone that is
associated to the embedding of M into V. The second purpose is to study
generalizations to smooth manifolds equipped with Lie filtrations. Following in
the footsteps of several others, we shall define a deformation to the normal
cone that is appropriate to this context, and relate it to Euler-like vector
fields and tubular neighborhood embeddings.
