This article is cited in 10 papers

On skew loops, skew branes and quadratic hypersurfaces

S. L. Tabachnikov

Department of Mathematics, Pennsylvania State University

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.

Key words and phrases: Skew loops and skew branes, quadratic hypersurfaces, double normals, Morse theory, developable surfaces.

MSC: 53A05, 53C50, 58E05

Language: English

DOI: 10.17323/1609-4514-2003-3-2-681-690

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