We study ruled submanifolds of Euclidean space. First, to each (parametrized) ruled submanifold σ, we associate an integer-valued function, called degree, measuring the extent to which σ fails to be cylindrical. In particular, we show that if the degree is constant and equal to d, then the singularities of σ can only occur along an (m-d)-dimensional "striction" submanifold. This result allows us to extend the standard classification of developable surfaces in R3 to the whole family of flat and ruled submanifolds without planar points, also known as rank-one: an open and dense subset of every rank-one submanifold is the union of cylindrical, conical, and tangent regions.
en
Project title:
Advanced Computational Design: F 77 (FWF Fonds zur Förderung der wissenschaftlichen Forschung (FWF))
