Functional Analysis and Its Applications

, Volume 42, Issue 2, pp 98–102 | Cite as

Topology of real algebraic curves

Article

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.

Key words

geodesic flow analytic first integral geodesic convexity M-curve 

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Copyright information

© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  1. 1.Steklov Mathematical InstituteRussia

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