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No skew branes on non-degenerate hyperquadrics

Ji-Ping Sha·Bruce Solomon
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Abstract

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.

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Ji-Ping Sha, Bruce Solomon. 2004-12-09. No skew branes on non-degenerate hyperquadrics. https://arxiv.org/abs/math/0412197

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