  The class of differential equations describing pseudospherical surfaces
enjoys important integrability properties which manifest themselves by the
existence of infinite hierarchies of conservation laws (both local and
non-local) and the presence associated linear problems. It thus contains many
important known examples of integrable equations, like the sine-Gordon,
Liouville, KdV, mKdV, Camassa-Holm and Degasperis-Procesi equations, and is
also home to many new families of integrable equations. Our paper is concerned
with the question of the local isometric immersion in ${\bf E}^{3}$ of the
pseudospherical surfaces defined by the solutions of equations belonging to the
class of Chern and Tenenblat. In the case of the sine-Gordon equation, it is a
classical result that the second fundamental form of the immersion depends only
on a jet of finite order of the solution of the pde. A natural question is
therefore to know if this remarkable property extends to equations other than
the sine-Gordon equation within the class of differential equations describing
pseudospherical surfaces. In the present paper, we consider third-order
equations of the form $u_{t}-u_{xxt}=\lambda u u_{xxx} + G(u,u_x,u_{xx}),\,
\lambda \in \mathbb{R}, $ which describe pseudospherical surfaces. This class
contains the Camassa-Holm and Degasperis-Procesi equations as special cases. We
show that whenever there exists a local isometric immersion in ${\bf E}^3$ for
which the coefficients of the second fundamental form depend on a jet of finite
order of $u$, then these coefficients are universal in the sense of being
independent on the choice of solution $u$.
