Bending and stretching unit vector fields in Euclidean and hyperbolic 3-space
Differential Geometry
2007-12-31 v2
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.
Keywords
Cite
@article{arxiv.math/0612286,
title = {Bending and stretching unit vector fields in Euclidean and hyperbolic 3-space},
author = {C. M. Wood},
journal= {arXiv preprint arXiv:math/0612286},
year = {2007}
}
Comments
18 pages