Linking, twisting, writhing and helicity on the 3-sphere and in hyperbolic 3-space

Details Linking, twisting, writhing and helicity on the 3-sphere and in hyperbolic 3-space Linking, twisting, writhing and helicity on the 3-sphere and in hyperbolic 3-space

2010-09-18

arxiv.org/abs/1009.3561v1

Mathematics

Geometric Topology

47 pages, 7 figures

Scientific paper

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.

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