E. Alves

activity

20162025

most citedResults on the homotopy type of the spaces of locally convex curves on

S^{3}

3 citations · 8 across the 7 of their papers we have counts for

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4 papers · 1 filter

math.GT2022

Homotopy type of spaces of locally convex curves in the sphere S^3

Emília Alves, Victor Goulart, Nicolau C. Saldanha

Locally convex (or nondegenerate) curves in the sphere $S^{n}$ have been studied for several reasons, including the study of linear ordinary differential equations of order $n + 1$ . Ta…

math.GT2020

Characterization of some convex curves on the 3-sphere

Emília Alves

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…

math.GT2017★ 3 cited

Results on the homotopy type of the spaces of locally convex curves on $S^{3}$

Emília Alves, Nicolau C. Saldanha

A curve $γ : [0, 1] \to S^{n}$ of class $C^{k}$ ( $k ⩾ n$ ) is locally convex if the vectors $γ (t), γ^{'} (t), γ " (t), \dots, γ^{(n)} (t)$ are a positive orthonormal basis to $R…

math.GT2016★ 3 cited

Topology of the space of locally convex curves on the 3-sphere

Emília Alves

A (positive) locally convex curve in the 2-sphere is a curve with positive geodesic curvature (i.e., which always turns left). In the 3-sphere, it is a curve with positive torsion.…

Homotopy type of spaces of locally convex curves in the sphere S^3

Characterization of some convex curves on the 3-sphere

Results on the homotopy type of the spaces of locally convex curves on S3

Topology of the space of locally convex curves on the 3-sphere

Results on the homotopy type of the spaces of locally convex curves on $S^{3}$