  We point out a new view on slow invariant manifolds (SIM) in dynamical
systems which departs from a purely geometric covariant characterization
implying coordinate independency. The fundamental idea is to treat the SIM as a
well-defined geometric object in phase space and elucidate characterizing
geometric properties that can be evaluated as point-wise analytic criteria. For
that purpose, we exploit curvature concepts and formulate our recent
variational approach in terms of coordinate-independent Hamiltonian
mechanics.Finally, we combine both approaches and conjecture a differential
geometric definition of slow invariant manifolds. For the Davis-Skodje model
the latter can be completely expatiated.
