  A recent work showing that homogeneous and isotropic cosmologies involving
scalar fields are equivalent to the geodesics of certain effective manifolds is
generalized to the non-minimally coupled and anisotropic cases. As the
Maupertuis-Jacobi principle in classical mechanics, such result permits us to
infer some dynamical properties of cosmological models from the geometry of the
associated effective manifolds, allowing us to go a step further in the study
of cosmological dynamics. By means of some explicit examples, we show how the
geometrical analysis can simplify considerably the dynamical analysis of
cosmological models.
