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arXiv · 1910.14523

A note on isometric immersions and differential equations which describe pseudospherical surfaces

Diego Catalano Ferraioli·Tarcísio Castro Silva·Keti Tenenblat
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Abstract

In this paper, we provide families of second order non-linear partial differential equations, describing pseudospherical surfaces (pss equations), with the property of having local isometric immersions in E^3, with principal curvatures depending on finite-order jets of solutions of the differential equation. These equations occupy a particularly special place amongst pss equations, since a series of recent papers [2, 7, 11, 12, 13], on several classes of pss equations, seemed to suggest that only the sine-Gordon equation had the above property. Explicit examples are given, which include the short pulse equation and some generalizations.

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Diego Catalano Ferraioli, Tarcísio Castro Silva, Keti Tenenblat. 2019-10-31. A note on isometric immersions and differential equations which describe pseudospherical surfaces. https://arxiv.org/abs/1910.14523

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