On skew loops, skew branes and quadratic hypersurfaces

Details On skew loops, skew branes and quadratic hypersurfaces On skew loops, skew branes and quadratic hypersurfaces

2003-02-21

arxiv.org/abs/math/0302263v1

Mathematics

Differential Geometry

13 pages, 2 figures

Scientific paper

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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