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

Nicolau C. Saldanha; Pedro Zühlke

doi:10.1142/s0129167x13501012

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arXiv · 1304.2629

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

Nicolau C. Saldanha·Pedro Zühlke

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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 $(κ_1,κ_2)$, in terms of $κ_1$ and $κ_2$. Many results concerning the topology of these spaces are established. In particular, we determine the homeomorphism class of some of these components.

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BibTeX RIS

Nicolau C. Saldanha, Pedro Zühlke. 2013-11-04. On the components of spaces of curves on the 2-sphere with geodesic curvature in a prescribed interval. https://doi.org/10.1142/s0129167x13501012

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