Linking, twisting, writhing and helicity on the 3-sphere and in hyperbolic 3-space
Geometric Topology
2010-09-21 v1
Abstract
We obtain explicit, isometry-invariant integral formulas for twisting, writhing and helicity, and prove the theorem LINK = TWIST + WRITHE on the 3-sphere and in hyperbolic 3-space. We then use these results to derive upper bounds for the helicity of vector fields and lower bounds for the first eigenvalue of the curl operator on subdomains of these two spaces.
Cite
@article{arxiv.1009.3561,
title = {Linking, twisting, writhing and helicity on the 3-sphere and in hyperbolic 3-space},
author = {Dennis DeTurck and Herman Gluck},
journal= {arXiv preprint arXiv:1009.3561},
year = {2010}
}
Comments
47 pages, 7 figures