On skew loops, skew branes and quadratic hypersurfaces

2003/02/21 by Serge Tabachnikov, Tabachnikov, Serge
Mathematics · #53A05 #53C50 #58E05 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53A05 #msc:53C50 #msc:58E05

paper · pdf · doi:10.48550/arxiv.math/0302263

13 pages, 2 figures

arxiv created 2003/02/21 · arxiv updated 2009/11/30

Abstract

A skew brane is an immersed codimension 2 submanifold in affine space, free from pairs of parallel tangent spaces. Using Morse theory, we prove that a skew brane cannot lie on a quadratic hypersurface. We also prove that there are no skew loops on embedded ruled developable discs in 3-space. The paper extends recent work by M. Ghomi and B. Solomon.

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• No skew branes on non-degenerate hyperquadrics
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