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

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dc.creatorWood, C. M.
dc.date2006-12-11
dc.date2007-12-31
dc.date.accessioned2026-07-07T08:51:39Z
dc.date.available2026-07-07T08:51:39Z
dc.descriptionNew 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.
dc.description18 pages
dc.identifierhttps://arxiv.org/abs/math/0612286
dc.identifierhttp://arxiv.org/abs/math/0612286
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/145008
dc.subjectDifferential Geometry
dc.subject53C43; 58E20
dc.titleBending and stretching unit vector fields in Euclidean and hyperbolic 3-space
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