  Tubular neighborhoods play an important role in differential topology. We
have applied these constructions to geometry of almost Hermitian manifolds. At
first, we consider deformations of tensor structures on a normal tubular
neighborhood of a submanifold in a Riemannian manifold.Further, an almost
hyperHermitian structure has been constructed on the tangent bundle TM with
help of the Riemannian connection of an almost Hermitian structure on a
manifold M then, we consider an embedding of the almost Hermitian manifold M in
the corresponding normal tubular neighborhood of the null section in the
tangent bundle TM equipped with the deformed almost hyperHermitian structure of
the special form.
  As a result,we have obtained that any smooth manifold M of dimension n can be
embedded as a totally geodesic submanifold in a Kaehlerian manifold of
dimension 2n and in a hyperKaehlerian manifold of dimension 4n.
