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On the geometric origin of the equation ϕ,11 — ϕ,22 = eϕ — e-2ϕ

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Abstract

It is shown that the equation ϕ,11 — ϕ,22 = eϕ — e-2ϕ determines the intrinsic geometry of the two-dimensional affine sphere in the three-dimensional unimodular affine space like the sine-Gordon equation describes the metric on the surface of a constant negative curvature in the three-dimensional Euclidean space. The linear equations that determine the moving frame on the affine sphere are the Lax operators to the equation ϕ,11 — ϕ,22 = eϕ — e-2ϕ.

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  1. Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980, Dubna, USSR

    V. V. Nesterenko

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  1. V. V. Nesterenko
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Nesterenko, V.V. On the geometric origin of the equation ϕ,11 — ϕ,22 = eϕ — e-2ϕ . Lett Math Phys 4, 451–456 (1980). https://doi.org/10.1007/BF00943430

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  • DOI: https://doi.org/10.1007/BF00943430

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