  We consider the $L^p \rightarrow L^q$ mapping properties of a model family of
Radon-like operators integrating functions over n-dimensional submanifolds of
${\mathbb R}^{2n}$. It is shown that nonvanishing rotational curvature is never
generic when $n \geq 2$ and is, in fact, impossible for all but finitely many
values of $n$. Nevertheless, operators satisfying the same $L^p \rightarrow
L^q$ estimates as the "nondegenerate" case (modulo the endpoint) are dense in
the model family for all $n$.
