3 papers
math.DG2023
A class of third order partial differential equations describing spherical or pseudospherical surfaces
Diego Catalano Ferraioli, Tarcísio Castro Silva
Third order equations, which describe spherical surfaces (ss) or pseudospherical surfaces (pss), of the form \[ ν\,z_{t}-λ\,z_{xxt}=A(z,z_{x},z_{xx})\,z_{xxx}+B(z,z_{x},z_{xx}) \]…
math.DG2019
A note on isometric immersions and differential equations which describe pseudospherical surfaces
Diego Catalano Ferraioli, Tarcísio Castro Silva, Keti Tenenblat
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…
math.DG2015
Third order differential equations and local isometric immersions of pseudospherical surfaces
Tarcísio Castro Silva, Niky Kamran
The class of differential equations describing pseudospherical surfaces enjoys important integrability properties which manifest themselves by the existence of infinite hierarchies…