No skew branes on non-degenerate hyperquadrics

We show that non-degenerate hyperquadrics in R^{n+2} admit no skew branes. Stated more traditionally, a compact codimension-one immersed submanifold of a non-degenerate hyperquadric of euclidean space must have parallel tangent spaces at two distinct points. Similar results have been proven by others, but (except for ellipsoids in R^3) always under C^2 smoothness and genericity assumptions. We use neither assumption here.