Skip to main content
Log in

Constructing isothermal curvature line coordinates on surfaces which admit them

  • Research Article
  • Published:
Central European Journal of Mathematics

Abstract

Isothermic parameterizations are synonyms of isothermal curvature line parameterizations, for surfaces immersed in Euclidean spaces. We provide a method of constructing isothermic coordinate charts on surfaces which admit them, starting from an arbitrary chart. One of the primary applications of this work consists of numerical algorithms for surface visualization.

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.

Similar content being viewed by others

References

  1. Bobenko A.I., Exploring surfaces through methods from the theory of integrable systems: the Bonnet problem, In: Surveys on Geometry and Integrable Systems, Adv. Stud. Pure Math., 51, Math. Soc. Japan, Tokyo, 2008, 1–53

    Google Scholar 

  2. do Carmo M.P., Differential Forms and Applications, Universitext, Springer, Berlin, 1994

    Book  MATH  Google Scholar 

  3. Chen W., Li H., Bonnet surfaces and isothermic surfaces, Results Math., 1997, 31(1–2), 40–52

    Article  MathSciNet  MATH  Google Scholar 

  4. Ivey T.A., Landsberg J.M., Cartan for Beginners, Grad. Stud. Math., 61, American Mathematical Society, Providence, 2003

    MATH  Google Scholar 

  5. Kose Z., Toda M., Aulisa E., Solving Bonnet problems to construct families of surfaces, Balkan J. Geom. Appl., 2011, 16(2), 70–80

    MathSciNet  MATH  Google Scholar 

  6. Lee J.M., Manifolds and Differential Geometry, Grad. Stud. Math., 107, American Mathematical Society, Providence, 2009

    MATH  Google Scholar 

  7. Pressley A., Elementary Differential Geometry, 2nd ed., Springer Undergrad. Math. Ser., Springer, London, 2010

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Eugenio Aulisa.

About this article

Cite this article

Aulisa, E., Toda, M. & Kose, Z.S. Constructing isothermal curvature line coordinates on surfaces which admit them. centr.eur.j.math. 11, 1982–1993 (2013). https://doi.org/10.2478/s11533-013-0289-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.2478/s11533-013-0289-6

MSC

Keywords

Navigation