  Let $\sigma$ be an involution of a real semi-simple Lie group $U$, $U_0$ the
subgroup fixed by $\sigma$, and $U/U_0$ the corresponding symmetric space.
Ferus and Pedit called a submanifold $M$ of a rank $r$ symmetric space $U/U_0$
a {\it curved flat} if $T_pM$ is tangent to an $r$-dimensional flat of $U/U_0$
at $p$ for each $p\in M$. They noted that the equation for curved flats is an
integrable system. Bryant used the involution $\sigma$ to construct an
involutive exterior differential system $\ci_\sigma$ such that integral
submanifolds of $\ci_\sigma$ are curved flats. Terng used $r$ first flows in
the $U/U_0$-hierarchy of commuting soliton equations to construct the
$U/U_0$-system. She showed that the $U/U_0$-system and the curved flat system
are gauge equivalent, used the inverse scattering theory to solve the Cauchy
problem globally with smooth rapidly decaying initial data, used loop group
factorization to construct infinitely many families of explicit solutions, and
noted that many these systems occur as the Gauss-Codazzi equations for
submanifolds in space forms. The main goals of this paper are: (i) give a
review of these known results, (ii) use techniques from soliton theory to
construct infinitely many integral submanifolds and conservation laws for the
exterior differential system $\ci_\sigma$.
