On skew loops, skew branes and quadratic hypersurfaces

Serge Tabachnikov

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On skew loops, skew branes and quadratic hypersurfaces

Serge Tabachnikov

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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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BibTeX RIS

Serge Tabachnikov. 2003-02-21. On skew loops, skew branes and quadratic hypersurfaces. https://arxiv.org/abs/math/0302263

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