The Gauss linking integral on the 3-sphere and in hyperbolic 3-space
| dc.creator | DeTurck, Dennis | |
| dc.creator | Gluck, Herman | |
| dc.date | 2004-06-14 | |
| dc.date.accessioned | 2026-07-07T05:09:13Z | |
| dc.date.available | 2026-07-07T05:09:13Z | |
| dc.description | We introduce here explicit integral formulas for linking, twisting, writhing and helicity on the 3-sphere and in hyperbolic 3-space. These formulas, like their prototypes in Euclidean 3-space, are geometric rather than just topological, in the sense that their integrands are invariant under orientation-preserving isometries of the ambient space. They are obtained by developing and then applying a steady-state version of classical electrodynamics in these two spaces, including an explicit Biot-Savart formula for the magnetic field and a corresponding Ampere's law contained in Maxwell's equations. The Biot-Savart formula leads, in turn, to upper bounds for the helicity of vector fields and lower bounds for the first eigenvalue of the curl operator on subdomains of the 3-sphere and hyperbolic 3-space. We give only a hint of the proofs. | |
| dc.identifier | https://arxiv.org/abs/math/0406276 | |
| dc.identifier | http://arxiv.org/abs/math/0406276 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71553 | |
| dc.subject | Geometric Topology | |
| dc.subject | Differential Geometry | |
| dc.subject | 57M25 (Primary), 53A99 (Secondary), 53Z05 | |
| dc.title | The Gauss linking integral on the 3-sphere and in hyperbolic 3-space | |
| dc.type | text |