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The global and local realizability of Bertrand Riemannian manifolds as surfaces of revolution

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Abstract

The problem of realizability as a surface of revolution embedded into ℝ3 is studied and solved for a two-dimensional Bertrand’s Riemannian manifold being a configuration space of an inverse problem of dynamics. The problem of local realizability (near a parallel) of those manifolds is also solved.

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References

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Moscow State University, Leninskie Gory, Moscow, 119991, Russia

    D. A. Fedoseev & O. A. Zagryadskii

Authors
  1. D. A. Fedoseev
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  2. O. A. Zagryadskii
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Corresponding author

Correspondence to D. A. Fedoseev.

Additional information

Original Russian Text © D.A. Fedoseev and O.A. Zagryadskii, 2015, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2015, Vol. 70, No. 3, pp. 18–24.

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Fedoseev, D.A., Zagryadskii, O.A. The global and local realizability of Bertrand Riemannian manifolds as surfaces of revolution. Moscow Univ. Math. Bull. 70, 119–124 (2015). https://doi.org/10.3103/S0027132215030043

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  • DOI: https://doi.org/10.3103/S0027132215030043

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