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On the geometric interpretation of solutions of a system generalizing the Sine-Gordon equation


We propose a geometric interpretation of solutions of the system generalizing the well-known sine-Gordon equation. We prove that to any solution of the Efimov-Poznyak system in a simply-connected domain, a C 3-smooth singular surface with given first fundamental bilinear form corresponds.

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Translated from Fundamental’naya i Prikladnaya Matematika (Fundamental and Applied Mathematics), Vol. 11, No. 1, Geometry, 2005.

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Bad’in, A.V. On the geometric interpretation of solutions of a system generalizing the Sine-Gordon equation. J Math Sci 141, 970–1003 (2007).

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  • Manifold
  • Bilinear Form
  • Geometric Interpretation
  • Geometric Object
  • Isometric Immersion