Skip to main content
SpringerLink
Log in

Time–like Linear Weingarten Surfaces in Lorentzian Space Forms

  • ORIGINAL ARTICLES
  • Published:
Acta Mathematica Sinica Aims and scope Submit manuscript

Abstract

In this paper we study Bäcklund transformations of time-like linear Weingarten surfaces with negative discriminant in Lorentzian space forms.

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. Eisenhart, L. P.: A treatise in the differential geometry of curves and surfaces., Ginn and Company, New York, 1909

  2. Chern, S. S., Terng, C. L.: An analogue of Bäcklund’s theorem in affine goemetry. Rocky Mountain J. Math., 10, 105–124 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  3. Chen, W. H., Li, H. Z.: Weingarten surfaces and [the] sine-Gordon equation. Science in China, A, 40, 1028–1035 (1997)

    MATH  Google Scholar 

  4. Tian, C., Cao, X. F.: Bäcklund transformations for surfaces with aK + bH = c. Chinese Ann. Math., Series A, 18(5), 529–538 (1997)

    Google Scholar 

  5. Chen, W. H., Li, H.: A remark on Bäcklund transformation of a Weingarten surfaces. Northeast Math. J., 15, 289–294 (1999)

    MATH  MathSciNet  Google Scholar 

  6. Gu, C. H., Hu, H. S., Zhou, Z. X.: Darboux Transformations in Soliton Theory and its Geometric Applications (in Chinese), Modern Mathematical Series, Shanghai Sci. Tech. Publ., 1999 (in Chinese)

  7. Milnor, T. K.: Surfaces in Minkowski 3-space on which H and K are linearly related. Michigan Math. J., 30, 309–312 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  8. Gu, C. H., Hu, H. S., Inoguchi, J.: On time-like surfaces of positive constant Gaussian curvature and imaginary principal curvatures. J. Geom. Phys., 41, 296–311 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  9. Zuo, D., Chen, Q., Cheng, Y.: Bäcklund theorems in three dimensional de Sitter space and anti-de Sitter space. J. Geom. Phys., 44, 279–298 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  10. Chen, W. H., Li, H.: Spacelike Weingarten surfaces in \( R^{3}_{1} \) and the sine-Gordon equation. J. Math. Anal. Appl., 214, 459–474 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  11. Cao, X. F., Tian, C.: B¨acklund transformations on surfaces with (k 1−m)(k 2−m) = ±l 2. J. Phys. A., 30, 6009–6020 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  12. Ma, H.: A note on Bäcklund transformations of timelike Weingarten surfaces in R 2,1. J. Math. Reseach Expositiion, 22, 89–95 (2002) (in Chinese)

    MATH  Google Scholar 

  13. Inoguchi, J.: Timelike surfaces of constant mean curvature in Minkowski 3-space. Tokyo J. Math., 21, 141–152 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  14. Inoguchi, J.: Darboux transformations on timelike constant mean curvature surface. J. Geom. Phys., 32, 57–78 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  15. Fujioka, A., Inoguchi, J.: Timelike Bonnet surfaces in Lorentzian space forms. Differential Geom. Appl., 18, 103–111 (2003)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, Tsinghua University, Beijing 100084, P. R. China

    Da Feng Zuo

  2. Department of Mathematics, University of Science and Technology of China, Anhui 230026, P. R. China

    Da Feng Zuo

Authors
  1. Da Feng Zuo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Da Feng Zuo.

Additional information

This work is partially supported by NSF 10301030 and NSF 10501043

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zuo, D.F. Time–like Linear Weingarten Surfaces in Lorentzian Space Forms. Acta Math Sinica 22, 1021–1026 (2006). https://doi.org/10.1007/s10114-005-0657-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10114-005-0657-7

Keywords

MR (2000) Subject Classification

Search

Navigation