The energy of unit vector fields on the 3-sphere

A. Higuchi; B.S. Kay; C.M. Wood

doi:10.1016/S0393-0440(00)00034-6

The energy of unit vector fields on the 3-sphere

A. Higuchi, B.S. Kay, C.M. Wood

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

The stability of the three-dimensional Hopf vector field, as a harmonic section of the unit tangent bundle is viewed from a number of different angles. The spectrum of the vertical Jacobi operator is computed, and compared with that of the Jacobi operator of the identity map on the 3-sphere. The variational behaviour of the three-dimensional Hopf vector field is compared and contrasted with that of the closely related Hopf map. Finally, it is shown chat the Hopf vector fields are the unique global minima of the energy functional restricted to unit vector fields on the 3-sphere. (C) 2001 Elsevier Science B.V. All rights reserved. MSG: 53C20; 53C15; 58E15; 58E20.

Original language	English
Pages (from-to)	137-155
Number of pages	19
Journal	Journal of Geometry and Physics
Volume	37
Issue number	1-2
DOIs	https://doi.org/10.1016/S0393-0440(00)00034-6
Publication status	Published - Jan 2001

Keywords

unit vector fields
3-sphere
HARMONIC MORPHISMS
FORMS
LAPLACIAN

Access to Document

10.1016/S0393-0440(00)00034-6

http://dx.doi.org/10.1016/S0393-0440(00)00034-6

Cite this

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title = "The energy of unit vector fields on the 3-sphere",

abstract = "The stability of the three-dimensional Hopf vector field, as a harmonic section of the unit tangent bundle is viewed from a number of different angles. The spectrum of the vertical Jacobi operator is computed, and compared with that of the Jacobi operator of the identity map on the 3-sphere. The variational behaviour of the three-dimensional Hopf vector field is compared and contrasted with that of the closely related Hopf map. Finally, it is shown chat the Hopf vector fields are the unique global minima of the energy functional restricted to unit vector fields on the 3-sphere. (C) 2001 Elsevier Science B.V. All rights reserved. MSG: 53C20; 53C15; 58E15; 58E20.",

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T1 - The energy of unit vector fields on the 3-sphere

AU - Higuchi, A.

AU - Kay, B.S.

AU - Wood, C.M.

PY - 2001/1

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N2 - The stability of the three-dimensional Hopf vector field, as a harmonic section of the unit tangent bundle is viewed from a number of different angles. The spectrum of the vertical Jacobi operator is computed, and compared with that of the Jacobi operator of the identity map on the 3-sphere. The variational behaviour of the three-dimensional Hopf vector field is compared and contrasted with that of the closely related Hopf map. Finally, it is shown chat the Hopf vector fields are the unique global minima of the energy functional restricted to unit vector fields on the 3-sphere. (C) 2001 Elsevier Science B.V. All rights reserved. MSG: 53C20; 53C15; 58E15; 58E20.

AB - The stability of the three-dimensional Hopf vector field, as a harmonic section of the unit tangent bundle is viewed from a number of different angles. The spectrum of the vertical Jacobi operator is computed, and compared with that of the Jacobi operator of the identity map on the 3-sphere. The variational behaviour of the three-dimensional Hopf vector field is compared and contrasted with that of the closely related Hopf map. Finally, it is shown chat the Hopf vector fields are the unique global minima of the energy functional restricted to unit vector fields on the 3-sphere. (C) 2001 Elsevier Science B.V. All rights reserved. MSG: 53C20; 53C15; 58E15; 58E20.

KW - unit vector fields

KW - 3-sphere

KW - HARMONIC MORPHISMS

KW - FORMS

KW - LAPLACIAN

U2 - 10.1016/S0393-0440(00)00034-6

DO - 10.1016/S0393-0440(00)00034-6

M3 - Article

VL - 37

SP - 137

EP - 155

JO - Journal of Geometry and Physics

JF - Journal of Geometry and Physics

IS - 1-2

ER -