# zbMATH — the first resource for mathematics

Bäcklund’s theorem for $$n$$-dimensional Lorentzian submanifold in the Minkowski space $$\mathbb E_1^{2n-1}$$. (English) Zbl 1335.53028
Authors’ 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 $$\mathbb E_1^{2n-1}$$.

##### MSC:
 53B25 Local submanifolds 53A35 Non-Euclidean differential geometry 53B30 Local differential geometry of Lorentz metrics, indefinite metrics 37K35 Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems 58J72 Correspondences and other transformation methods (e.g., Lie-Bäcklund) for PDEs on manifolds
##### Keywords:
Bäcklund theorem; Minkowski space; Lorentzian submanifold
Full Text:
##### 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) · Zbl 0407.53002 [2] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. Johns Hopkins University Press, Baltimore, Maryland (1996). ISBN:0-8018-5414-8 · Zbl 0865.65009 [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 · Zbl 1084.37054 [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) · Zbl 0866.53049 [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) · Zbl 0462.35079 [6] Eısenhart L.P.: A Treatise in the Differential Geometry of Curves and Surfaces. Ginn Camp, New York (1969) [7] Chern, S.S.; Terng, C.L., An analogue of Bäcklund’s theorem in affine geometry, Rocky Mt. J. Math., 10, 105-124, (1980) · Zbl 0407.53002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.