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Topology of real algebraic curves

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Functional Analysis and Its Applications Aims and scope

An Erratum to this article was published on 01 July 2008

Abstract

The problem on the existence of an additional first integral of the equations of geodesics on noncompact algebraic surfaces is considered. This problem was discussed as early as by Riemann and Darboux. We indicate coarse obstructions to integrability, which are related to the topology of the real algebraic curve obtained as the line of intersection of such a surface with a sphere of large radius. Some yet unsolved problems are discussed.

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Authors and Affiliations

  1. Steklov Mathematical Institute, Russia

    V. V. Kozlov

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  1. V. V. Kozlov
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Correspondence to V. V. Kozlov.

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__________

Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 42, No. 2, pp. 23–27, 2008

Original Russian Text Copyright © by V. V. Kozlov

An erratum to this article is available at http://dx.doi.org/10.1007/s10688-008-0038-y.

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Kozlov, V.V. Topology of real algebraic curves. Funct Anal Its Appl 42, 98–102 (2008). https://doi.org/10.1007/s10688-008-0015-5

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  • DOI: https://doi.org/10.1007/s10688-008-0015-5

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