Characterization of some convex curves on the 3-sphere

2020/02/10 by Emília Alves, Alves, Emília
Mathematics · #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2002.03986

openalex publication_date 2020/02/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we provide a characterization for a class of convex curves on the 3-sphere. More precisely, using a theorem that decomposes a locally convex curve on the 3-sphere as a pair of curves on the 2-sphere, one of which is locally convex and the other is an immersion, we are capable of completely characterize a class of convex curves on the 3-sphere.

Citations

• On Curves of Minimal Length with a Constraint on Average Curvature, and with Prescribed Initial and Terminal Positions and Tangents

Related

• Topology of the space of locally convex curves on the 3-sphere
• On two conjectures concerning convex curves
• On the convex hull of a space curve
• The homotopy and cohomology of spaces of locally convex curves in the sphere -- II
• Shortest closed curve to contain a sphere in its convex hull