ON THE COMPONENTS OF SPACES OF CURVES ON THE 2-SPHERE WITH GEODESIC CURVATURE IN A PRESCRIBED INTERVAL

DOI10.1142/S0129167X13501012zbMath1288.53054arXiv1304.2629MaRDI QIDQ5401592

Nicolau C. Saldanha, Pedro Zühlke

Publication date: 10 March 2014

Published in: International Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1304.2629

zbMATH Keywords

curvegeodesic curvaturehomotopytopology of infinite-dimensional manifolds

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Curves in Euclidean and related spaces (53A04) Topology of infinite-dimensional manifolds (57N20)

Related Items (7)

Stratification of spaces of locally convex curves by itineraries ⋮ Results on the homotopy type of the spaces of locally convex curves on $\mathbb{S}^3$ ⋮ Spaces of curves with constrained curvature on hyperbolic surfaces ⋮ Homotopical and topological rigidity of hypersurfaces of spherical space forms ⋮ The geometry of \(C^1\) regular curves in sphere with constrained curvature ⋮ On the space of \(C^1\) regular curves on sphere with constrained curvature ⋮ The homotopy type of spaces of locally convex curves in the sphere

Cites Work

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• Nondegenerate curves on \(S^ 2\) and orbit classification of the Zamolodchikov algebra
• Results on infinite-dimensional topology and applications to the structure of the critical set of nonlinear Sturm--Liouville operators
• Homotopy theory of infinite dimensional manifolds
• Nondegenerate homotopies of curves on the unit 2-sphere
• On the number of connected components in the space of closed nondegenerate curves on 𝑆_{𝑛}
• Infinite-dimensional manifolds are open subsets of Hilbert space

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