No skew branes on non-degenerate hyperquadrics
Abstract
We show that non-degenerate hyperquadrics in Rn+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 R3) always under C2 smoothness and genericity assumptions. We use neither assumption here.
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