Poincaré index and the volume functional of unit vector fields on punctured spheres

DOI10.1007/S00229-019-01107-YzbMath1433.53056arXiv1708.01575OpenAlexW2964297644WikidataQ122111947 ScholiaQ122111947MaRDI QIDQ2297364

André O. Gomes, Icaro Gonçalves, Fabiano Gustavo Braga Brito

Publication date: 18 February 2020

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1708.01575

zbMATH Keywords

isolated singularitiesPoincaré indices

Mathematics Subject Classification ID

Vector fields, frame fields in differential topology (57R25) Global Riemannian geometry, including pinching (53C20) Foliations (differential geometric aspects) (53C12)

Related Items (4)

Vector fields with big and small volume on the \(2\)-sphere ⋮ Minimally immersed Klein bottles in the unit tangent bundle of the unit 2-sphere arising from area-minimizing unit vector fields on \(\mathbb{S}^2\backslash \{ N,S\}\) ⋮ Calibrations for the volume of unit vector fields in dimension 2 ⋮ Area minimizing unit vector fields on antipodally punctured unit 2-sphere

Cites Work

• Lower bounds on volumes of vector fields
• Energy and topology of singular unit vector fields on S\(^{3}\)
• On the volume of a unit vector field on the three-sphere
• On the volume of unit vector fields on spaces of constant sectional curvature
• A critical radius for unit Hopf vector fields on spheres
• A topological minorization for the volume of vector fields on 5-manifolds
• A simple intrinsic proof of the Gauss-Bonnet formula for closed Riemannian manifolds
• On the curvatura integra in a Riemannian manifold
• Unit vector fields on antipodally punctured spheres: big index, big volume
• Area-minimizing vector fields on round 2-spheres
• Volumes of Vector Fields on Spheres
• Volumes of Flows

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