By the same authors

Bending and stretching unit vector fields in Euclidean and hyperbolic 3-space

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JournalAnnals of Global Analysis and Geometry
DatePublished - Sep 2008
Issue number2
Volume34
Number of pages13
Pages (from-to)101-113
Original languageEnglish

Abstract

New examples of harmonic unit vector fields on hyperbolic 3-space are constructed by exploiting the reduction of symmetry arising from the foliation by horospheres. This is compared and contrasted with the analogous construction in Euclidean 3-space, using a foliation by planes, which produces some new examples of harmonic maps from 3-dimensional Euclidean domains to the 2-sphere. Finally, the harmonic unit vector field tangent to a parallel family of hyperbolic geodesics is shown to be unstable, by constructing a class of compactly supported energy-decreasing variations. All examples considered have infinite total bending.

    Research areas

  • harmonic section, harmonic map, harmonic unit vector field, harmonic function, sine-gordon equation, pendulum equation, horospheres, energy, bending, unstable, stretchable, RIEMANNIAN-MANIFOLDS, HARMONIC MAPPINGS, ENERGY, VOLUME

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