Volume minimising unit vector fields on three dimensional space forms of positive curvature

We prove that on a closed 3-manifold of constant positive curvature the unit vector fields of minimum volume are exactly the Hopf vector fields.

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Bibliographic Details
Published in:Calculus of variations and partial differential equations 2022-04, Vol.61 (2), Article 66
Main Author: Gil-Medrano, Olga
Format: Article
Language:English
Subjects:
Analysis
Calculus of Variations and Optimal Control
Optimization
Control
Curvature
Fields (mathematics)
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Systems Theory
Theoretical
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Description
Summary:We prove that on a closed 3-manifold of constant positive curvature the unit vector fields of minimum volume are exactly the Hopf vector fields.
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-021-02177-1