  We consider the class of differential equations that describe
pseudo-spherical surfaces of the form $u\_t=F(u,u\_x,u\_{xx})$ and
$u\_{xt}=F(u, u\_x)$ given in Chern-Tenenblat \cite{ChernTenenblat} and
Rabelo-Tenenblat \cite{RabeloTenenblat90}. We answer the following question:
Given a pseudo-spherical surface determined by a solution $u$ of such an
equation, do the coefficients of the second fundamental form of the local
isometric immersion in $\mathbb{R}^3$ depend on a jet of finite order of $u$?
We show that, except for the sine-Gordon equation, where the coefficients
depend on a jet of order zero, for all other differential equations, whenever
such an immersion exists, the coefficients are universal functions of $x$ and
$t$, independent of $u$.
