Components of spaces of curves with constrained curvature on flat surfaces

Abstract

Let $S$ be a complete 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.

arXiv commentFinal version, to appear in Pacific J. Math., 39 pages, 10 figures. Version 3 contains additional results in section 7 which were omitted from the present version for the sake of conciseness

References in corpus (2)

• On the components of spaces of curves on the 2-sphere with geodesic curvature in a prescribed interval
• The homotopy type of spaces of locally convex curves in the sphere

Cited by in corpus (2)

• On a class of immersions of spheres into space forms of nonpositive curvature
• Characterization of some convex curves on the 3-sphere