  This is the content of a talk given by the author at the 2009 Lehigh
University Geometry/Topology Conference.
  Using the definition of connection given by Dieudonn\'e, the Sasaki metric on
the tangent bundle to a Riemannian manifold is expressed in a natural way.
  Also, the following property is established. The induced metric on the
tangent bundle of an isometrically embedded submanifold is the Sasaki metric if
and only if the submanifold is totally geodesic.
