  Assuming a-priori a smooth generating vector field, we introduce a generally
covariant measure of the flow geometry called the referential gradient of the
flow. The main result is the explicit relation between the referential gradient
and the generating vector field, and is provided for from two equivalent
perspectives: a Lagrangian specification with respect to a generalized
parameter, and an Eulerian specification making explicit the evolution
dynamics. Furthermore, we provide explicit non-trivial conditions which govern
the transformation properties of the referential gradient object.
