Skip to main content
SpringerLink
Log in

On constant mean curvature surfaces in the Heisenberg group

  • Published:
Siberian Advances in Mathematics Aims and scope Submit manuscript

Abstract

This work is devoted to the theory of surfaces of constant mean curvature in the three-dimensional Heisenberg group. It is proved that each surface of such a kind locally corresponds to some solution of the system of a sine-Gordon type equation and a first order partial differential equation.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. U. Abresch, “Constant mean curvature tori in terms of elliptic functions,” J. Reine Angew. Math. 374, 169–192 (1987).

    MathSciNet  MATH  Google Scholar 

  2. U. Abresch and H. Rosenberg, “Generalized Hopf differentials,” Mat. Contemp. 28, 1–28 (2005).

    MathSciNet  MATH  Google Scholar 

  3. D. A. Berdinsky and I. A. Taimanov, “Surfaces in three-dimensional Lie groups,” Siberian Math. J. 46(6), 1005–1019 (2005).

    Article  MathSciNet  Google Scholar 

  4. P. Scott, “The geometries of 3-manifolds,” Bull. London Math. Soc. 15(5), 401–487 (1983).

    Article  MathSciNet  MATH  Google Scholar 

  5. I. A. Taimanov, “Dirac operators and conformal invariants of tori in three-dimensional space,” Proc. Steklov Inst. Math. ((244)), 233–263 (2004).

  6. I. A. Taimanov, “Surfaces in three-dimensional Lie groups in terms of spinors,” RIMS Kokyuroku 1605, 133–150 (2008).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, 630090, Russia

    D. A. Berdinsky

Authors
  1. D. A. Berdinsky
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to D. A. Berdinsky.

Additional information

Original Russian Text © D. A. Berdinsky, 2010, published in Matematicheskie Trudy, 2010, Vol. 13, No. 2, pp. 3–9.

About this article

Cite this article

Berdinsky, D.A. On constant mean curvature surfaces in the Heisenberg group. Sib. Adv. Math. 22, 75–79 (2012). https://doi.org/10.3103/S1055134412020010

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1055134412020010

Keywords

Search

Navigation