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

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.

47 pages, 7 figures

References in corpus (1)

• The Gauss linking integral on the 3-sphere and in hyperbolic 3-space

Cited by in corpus (1)

• Higher dimensional abelian Chern-Simons theories and their link invariants