On the components of spaces of curves on the 2-sphere with geodesic curvature in a prescribed interval

Abstract

We obtain simple characterizations of the connected components of the space of closed curves on the 2-sphere whose geodesic curvatures are constrained to lie in an open interval $({\kappa }_1,{\kappa }_2)$, in terms of ${\kappa }_1$ and ${\kappa }_2$. Many results concerning the topology of these spaces are established. In particular, we determine the homeomorphism class of some of these components.

arXiv comment54 pages, 16 figures. In this version, the introduction has been expanded and a couple of comments relating this work to that of other authors have been added. Other modifications concern either the correction of small mistakes or improvements of the exposition. Proofs have not been changed

References in corpus (4)

• The homotopy and cohomology of spaces of locally convex curves in the sphere -- II
• The space of non-degenerate closed curves in a Riemannian manifold
• Homotopies of Curves on the 2-Sphere with Geodesic Curvature in a Prescribed Interval
• The homotopy and cohomology of spaces of locally convex curves in the sphere -- I

Cited by in corpus (8)

• The homotopy type of spaces of locally convex curves in the sphere
• Combinatorialization of spaces of nondegenerate spherical curves
• Components of spaces of curves with constrained curvature on flat surfaces
• Spaces of curves with constrained curvature on hyperbolic surfaces
• Stratification of spaces of locally convex curves by itineraries
• Homotopical and topological rigidity of hypersurfaces of spherical space forms
• Characterization of some convex curves on the 3-sphere
• On the Space of $C^1$ Regular Curves on Sphere with Constrained Curvature