A note on isometric immersions and differential equations which describe pseudospherical surfaces
Differential Geometry
2022-01-28 v2
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.
Keywords
Cite
@article{arxiv.1910.14523,
title = {A note on isometric immersions and differential equations which describe pseudospherical surfaces},
author = {Diego Catalano Ferraioli and Tarcísio Castro Silva and Keti Tenenblat},
journal= {arXiv preprint arXiv:1910.14523},
year = {2022}
}