Components of spaces of curves with constrained curvature on flat surfaces

Nicolau C. Saldanha; Pedro Zühlke

doi:10.2140/pjm.2016.281.185

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arXiv · 1312.1675

Components of spaces of curves with constrained curvature on flat surfaces

Nicolau C. Saldanha·Pedro Zühlke

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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.

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BibTeX RIS

Nicolau C. Saldanha, Pedro Zühlke. 2013-12-05. Components of spaces of curves with constrained curvature on flat surfaces. https://doi.org/10.2140/pjm.2016.281.185

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