No skew branes on non-degenerate hyperquadrics

2004/12/09 by Ji-Ping Sha, Sha, Ji-Ping, Bruce Solomon +1
Mathematics · #53C40 #57R42 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53C40 #msc:57R42

paper · pdf · doi:10.48550/arxiv.math/0412197

6 pages

arxiv created 2004/12/09 · arxiv updated 2009/12/01

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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