On the topology of the spaces of curvature constrained plane curves
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José Ayala
Abstract
Plane curves with the same endpoints are homotopic; an analogous claim for plane curves with the same endpoints and bounded curvature still remains open. We find necessary and sufficient conditions for two plane curves with bounded curvature to be deformed into each other by a continuous one-parameter family of curves also having bounded curvature. We conclude that the space of these curves has either one or two connected components, depending on the distance between the endpoints. The classification theorem presented here answers a question raised in 1961 by L. E. Dubins.
Acknowledgements
I would like to thank both reviewers for their thorough comments and suggestions, particularly the second reviewer for the many efforts on behalf of the manuscript.
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© 2017 by Walter de Gruyter Berlin/Boston
Articles in the same Issue
- Frontmatter
- Classification of 3-dimensional left-invariant almost paracontact metric structures
- On the topology of the spaces of curvature constrained plane curves
- On deformations of parallel G2 structures and almost contact metric structures
- A flag representation of projection functions
- A fundamental theorem for submanifolds of multiproducts of real space forms
- Intriguing sets of quadrics in PG(5, q)
- Successive radii and ball operators in generalized Minkowski spaces
- Optimal inequalities for the normalized δ-Casorati curvatures of submanifolds in Kenmotsu space forms
- The Archimedean projection property
- Kernels of numerical pushforwards
- Modified classical flat Minkowski planes
Articles in the same Issue
- Frontmatter
- Classification of 3-dimensional left-invariant almost paracontact metric structures
- On the topology of the spaces of curvature constrained plane curves
- On deformations of parallel G2 structures and almost contact metric structures
- A flag representation of projection functions
- A fundamental theorem for submanifolds of multiproducts of real space forms
- Intriguing sets of quadrics in PG(5, q)
- Successive radii and ball operators in generalized Minkowski spaces
- Optimal inequalities for the normalized δ-Casorati curvatures of submanifolds in Kenmotsu space forms
- The Archimedean projection property
- Kernels of numerical pushforwards
- Modified classical flat Minkowski planes
