Spaces of Curves with Constrained Curvature on Flat Surfaces, I
نویسنده
چکیده
Let S be a flat surface, such as the Euclidean plane. We obtain direct characterizations of the connected components of the space of all curves on S which start and end at given points in given directions, and whose curvatures are constrained to lie in a given interval, in terms of all parameters involved. Many topological properties of these spaces are investigated. Some conjectures of L. E. Dubins are proved.
منابع مشابه
Homotopy Type of Spaces of Curves with Constrained Curvature on Flat Surfaces
Let S be a complete flat surface, such as the Euclidean plane. We determine the homeomorphism class of the space of all curves on S which start and end at given points in given directions and whose curvatures are constrained to lie in a given open interval, in terms of all parameters involved. Any connected component of such a space is either contractible or homotopy equivalent to an n-sphere, ...
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تاریخ انتشار 2013