Laplace transformation in higher dimensions

DOI10.1215/S0012-7094-96-08409-4zbMath0857.53004OpenAlexW2088721287MaRDI QIDQ1922426

Niky Kamran, Keti Tenenblat

Publication date: 30 October 1996

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-96-08409-4

zbMATH Keywords

Euclidean spaceLaplace transformationDarboux invariantconjugate netCartan varietysecond-order overdetermined system of partial differential equations

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Laplace transform (44A10) Global Riemannian geometry, including pinching (53C20) Second-order hyperbolic equations (35L10) Correspondences and other transformation methods (e.g., Lie-Bäcklund) for PDEs on manifolds (58J72) Overdetermined problems for partial differential equations and systems of partial differential equations (35N99)

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On Dupin hypersurfaces in \(\mathbb R^{5}\) parametrized by lines of curvature, Laplace maps and constraints for a class of third-order partial differential operators, Dupin hypersurfaces with four principal curvatures in \(\mathbb R^{5}\) with principal coordinates, On a class of Dupin hypersurfaces in \(\mathbb R^5\) with nonconstant Lie curvature, Exterior differential systems and Cartan-Kähler theory, The variational bi-complex for systems of semi-linear hyperbolic PDEs in three variables, On four dimensional Dupin hypersurfaces in Euclidean space, Method for Solving the Multidimensional n-Wave Resonant Equations and Geometry of Generalized Darboux-Manakov-Zakharov Systems, Laplace transformations of hydrodynamic-type systems in Riemann invariants, Laplace Transformation of Lie Class ω = 1 Overdetermined Systems, The multidimensional Darboux transformation, Darboux transformations and \(\mathcal D\)-modules, Proceedings of the 12th international workshop on nonlinear evolution equations and dynamical systems (NEEDS '98), Leeds, UK, June 21--28, 1998. Transl. from the Russian, The conjugate nets, Cartan submanifolds, and Laplace transformations in space forms

Cites Work

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• Bäcklund's theorem for \(n\)-dimensional submanifolds of \(R^{2n-1}\)
• Bäcklund transformations for a class of systems of differential equations
• On the Solution of the Generalized Wave and Generalized Sine-Gordon Equations
• Oscillations of the zero dispersion limit of the korteweg‐de vries equation
• THE GEOMETRY OF HAMILTONIAN SYSTEMS OF HYDRODYNAMIC TYPE. THE GENERALIZED HODOGRAPH METHOD
• Bäcklund's theorem for submanifolds of space forms and a generalized wave equation
• Laplace Transforms of a Class of Higher Dimensional Varieties in a Projective Space of n Dimensions