  We study the geometric properties of the energy landscape of coarse-grained,
off-lattice models of polymers by endowing the configuration space with a
suitable metric, depending on the potential energy function, such that the
dynamical trajectories are the geodesics of the metric. Using numerical
simulations, we show that the fluctuations of the curvature clearly mark the
folding transition, and that this quantity allows to distinguish between
polymers having a protein-like behavior (i.e., that fold to a unique
configuration) and polymers which undergo a hydrophobic collapse but do not
have a folding transition. These geometrical properties are defined by the
potential energy without requiring any prior knowledge of the native
configuration.
