Skip to main content
Log in

Bäcklund’s Theorem for n Dimensional Lorentzian Submanifold in the Minkowski Space \({\mathbb{E}_1^2n-1}\)

  • Published:
Results in Mathematics Aims and scope Submit manuscript

Abstract

In this paper, Bäcklund’s Theorem is introduced on the Lorentzian n-submanifold of the Minkowski space \({\mathbb{E}_{1}^{2n-1}}\) by using the method of moving frames. Also, we prove the Integrability Theorem for the Lorentzian n-submanifold of the Minkowski space \({\mathbb{E}_{1}^{2n-1}}\).

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. Chen, W., Li, H., Ma, H.: Isometric Immersions of Indefinite Space Forms in Indefinite Space Forms. Advances in Mathematics, vol. 34, no. 5 (2005)

  2. Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. Johns Hopkins University Press, Baltimore, Maryland (1996). ISBN:0-8018-5414-8

  3. Gu, C., Hu, H., Zhou, Z.: Darboux Transformations in Integrable Systems Theory and Their Applications to Geometry. Mathematical Physics Studies, vol. 26, Springer (2005). doi:10.1007/1-4020-3088-6

  4. Barbosa J.L., Ferreira W., Tenenblat K.: Submanifolds of constant sectional curvature in pseudo-Riemann manifolds. Ann. Global Anal. Geom. 14, 381–401 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  5. Tenenblat, K., Terng, C.L.: Bäcklund’s theorem for n-dimensional Submanifold of \({\mathbb{R}^{2n-1}}\). Annals of Mathematics, Second Series, vol. 111, no. 3, pp. 477–490 (1980)

  6. Eısenhart L.P.: A Treatise in the Differential Geometry of Curves and Surfaces. Ginn Camp, New York (1969)

    Google Scholar 

  7. Chern S.S., Terng C.L.: An analogue of Bäcklund’s theorem in affine geometry. Rocky Mt. J. Math. 10(1), 105–124 (1980)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Hakan Simsek.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Simsek, H., Özdemir, M. Bäcklund’s Theorem for n Dimensional Lorentzian Submanifold in the Minkowski Space \({\mathbb{E}_1^2n-1}\) . Results. Math. 69, 201–223 (2016). https://doi.org/10.1007/s00025-015-0479-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00025-015-0479-6

Mathematics Subject Classification

Keywords

Navigation