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

Title	Bending and stretching unit vector fields in Euclidean and hyperbolic 3-space
Publication Type	Journal Article
Year of Publication	2008
Authors	Wood C
Journal	Annals of Global Analysis and Geometry
Volume	34
Start Page	101
Pagination	101-113
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 unit vector field tangent to a parallel family of hyperbolic geodesics is shown to be unstable, by constructing a class of compactly supported eneergy decreasing variations. All examples considered have infinite total bending.
URL	http://arxiv.org/abs/math/0612286v2
DOI	10.1007/s10455-008-9102-3
E-print number	arXiv:math/0612286v2

Department of Mathematics