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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
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