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arXiv · 2212.01922

On certain properties of pseudo-Riemannian Bertrand manifolds

D. A. Fedoseev
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Abstract

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.

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D. A. Fedoseev. 2022-12-04. On certain properties of pseudo-Riemannian Bertrand manifolds. https://arxiv.org/abs/2212.01922

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