  In the present article we prove and discuss several properties of
pseudo-Riemannian Bertrand manifolds, and give an overview of the state of the
theory together with problems for future work. In particular, we prove that
there are no pseudo-Riemannian completely Bertrand systems -- dynamical systems
of movement in a central field on a pseudo-Riemannian 2-dimensional manifold of
revolution such that all trajectories of movement are closed.
