No skew branes on non-degenerate hyperquadrics
Differential Geometry
2007-05-23 v1
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.
Keywords
Cite
@article{arxiv.math/0412197,
title = {No skew branes on non-degenerate hyperquadrics},
author = {Ji-Ping Sha and Bruce Solomon},
journal= {arXiv preprint arXiv:math/0412197},
year = {2007}
}
Comments
6 pages