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). https://doi.org/10.1007/s10958-007-0026-4
- Bilinear Form
- Geometric Interpretation
- Geometric Object
- Isometric Immersion