Skip to main content

Curves on Surfaces

  • Chapter
Foliations on Surfaces

Part of the book series: Ergebnisse der Mathematik und ihrer Grenzgebiete ((MATHE3,volume 41))

  • 689 Accesses

Abstract

Every foliation on the surface is a union of curves. It is therefore logical to pay special attention to curves. On the other hand, the behaviour of curves without self-intersections on surfaces is a problem of independent interest.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliographic Notes

  1. Anosov, D. V. 1995 Flows on closed surfaces and behavior of trajectories lifted to the universal covering plane, J. of Dynamical and Control Syst. 1, 125–138.

    Google Scholar 

  2. Weil, A., 1931 On systems of curves on a ring-shaped surface, J. of the Indian Math. Soc. 19, No.5, 109–112; No. 6, 113–114.

    Google Scholar 

  3. Weil, A., 1936 Les familles de courbes sur le tore, Mat. Sbornik 1, No 5, 779–781.

    Google Scholar 

  4. Pupko, V. I., 1967 Non-self-intersecting curves on closed surfaces, Dokl. Akad. Nauk SSSR 177, 272–274.

    MathSciNet  Google Scholar 

  5. Aranson, S. H. and Grines V. Z., 1973 On certain invariants of dynamical systems on two-dimensional manifolds (necessary and sufficient conditions of topological equivalence of transitive systems), Mat. Sb. 90, 372–402.

    MathSciNet  Google Scholar 

  6. Anosov, D. V. 1987 On the behavior in the Euclidean or Lobachevsky plane of the trajectories that cover trajectories of flows on closed surfaces. I, Math. USSR Izvestiya 51, 16–43.

    MathSciNet  MATH  Google Scholar 

  7. Anosov, D. V. 1988 On the behavior in the Euclidean or Lobachevsky plane of the trajectories that cover trajectories of flows on closed surfaces. II, Math. USSR Izvestiya 52, 451–478.

    Google Scholar 

  8. Anosov, D. V. 1990 Infinite curves on the torus and on closed surfaces of negative Euler characteristic, Proc. Steklov Math. Inst. 185, 33–58.

    MATH  Google Scholar 

  9. Anosov, D. V. 1992 How curves on the universal covering plane that cover non-selfintersecting curves on a closed surface can go to infinity, Proc. Steklov Math. Inst. 191, 35–45.

    Google Scholar 

  10. Anosov, D. V. 1995 Flows on closed surfaces and behavior of trajectories lifted to the universal covering plane, J. of Dynamical and Control Syst. 1, 125–138.

    Google Scholar 

  11. Whitney, H., 1933 Regular families of curves, Ann. of Math. 34, 244–270.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Nikolaev, I. (2001). Curves on Surfaces. In: Foliations on Surfaces. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol 41. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04524-4_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-04524-4_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-08698-4

  • Online ISBN: 978-3-662-04524-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics