Skip to main content
Log in

A gallery of constant-negative-curvature surfaces

  • Article
  • Published:
The Mathematical Intelligencer Aims and scope Submit manuscript

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. M. J. Ablowitz, D. J. Kaup, A. C. Newell, and H. Segur, Method for solving the sine-Gordon equation,Phys. Rev. Lett. 30 (1973), 191–193.

    Article  MathSciNet  Google Scholar 

  2. M. J. Ablowitz and H. Segur,Solitons and the Inverse Scattering Transform, Philadelphia: SIAM, (1981).

    Book  MATH  Google Scholar 

  3. Visualizations were done in geomview, available from the Geometry Center, Minneapolis, by anonymous ftp to geom.umn.edu.

  4. L. P. Eisenhart,A Treatise on the Differential Geometry of Curves and Surfaces, New York: Dover (1960) (originally published 1909).

    MATH  Google Scholar 

  5. Gerd Fischer,Mathematische Modelle, Braunschweig Wiesbaden Vieweg, 2 vols. (1986).

  6. H. Hasimoto, A soliton on a vortex filament,J. Fluid Mech. 51 (1972), 477–485.

    Article  MATH  Google Scholar 

  7. J. N. Hazzidakis, Ueber einige Eigenschaften der Flächen mit constantem Krümmungsmaass,J. reine angew. Math. (“Crelle’s Journal”) 88 (1880), 68–73.

    Google Scholar 

  8. D. Hilbert, Ueber Flächen von constanter Gaussscher Krümmung,Trans. Amer. Math. Soc. 2 (1901), 87–99.

    MATH  MathSciNet  Google Scholar 

  9. S. B. Kadomtsev, Surfaces with constant exterior geometry of negative curvature,Math. Notes Acad. Sci. USSR 47(4) (1990), 339–341.

    Article  MATH  MathSciNet  Google Scholar 

  10. G. L. Lamb Jr.,, Solitons on moving space curves,J. Math. Phys. 18(8) (1977), 1654–1661.

    Article  MATH  MathSciNet  Google Scholar 

  11. M. Melko and I. Sterling, Application of soliton theory to the construction of pseudospherical surfaces in R3,Ann. Global Anal. Geom. 11(1) (1993), 65–107.

    Article  MATH  MathSciNet  Google Scholar 

  12. K. Nakayama, H. Segur, and M. Wadati, Integrability and the motion of curves,Phys. Rev. Lett. 69 (1992), 2603–2606.

    Article  MATH  MathSciNet  Google Scholar 

  13. A. Seeger, H. Donth, and A. Kochendörfer, Théorie der Versetzungen in eindimensionalen Atomreihen. III: Ver- setzungen, Eigenbewegungen und ihre Wechselwirkung, Z.Phys. 134 (1953), 173–193.

    Article  MATH  Google Scholar 

  14. H. Segur, Who cares about integrability?,Physica D 51 (1991), 343–359.

    Article  MATH  MathSciNet  Google Scholar 

  15. H. Segur, personal communication.

  16. J. J. Stoker,Differential Geometry, New York: Wiley- Interscience (1969).

    MATH  Google Scholar 

  17. M. Spivak,A Comprehensive Introduction to Differential Geometry, Volume III, Boston: Publish or Perish, Inc. (1975).

  18. P. L. Tchebychev,Sur la coupe des větements(1878), (Œuvres, vol. II, New York: Chelsea (1962), 708.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

McLachlan, R. A gallery of constant-negative-curvature surfaces. The Mathematical Intelligencer 16, 31–37 (1994). https://doi.org/10.1007/BF03024701

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03024701

Keywords

Navigation