Rotations of the three-sphere and symmetry of the Clifford torus
| dc.creator | McCuan, John | |
| dc.creator | Spietz, Lafe | |
| dc.date | 1998-10-05 | |
| dc.date.accessioned | 2026-07-07T05:26:18Z | |
| dc.date.available | 2026-07-07T05:26:18Z | |
| dc.description | We describe decomposition formulas for rotations of $R^3$ and $R^4$ that have special properties with respect to stereographic projection. We use the lower dimensional decomposition to analyze stereographic projections of great circles in $S^2 \subset R^3$. This analysis provides a pattern for our analysis of stereographic projections of the Clifford torus ${\mathcal C}\subset S^3 \subset R^4$. We use the higher dimensional decomposition to prove a symmetry assertion for stereographic projections of ${\mathcal C}$ which we believe we are the first to observe and which can be used to characterize the Clifford torus among embedded minimal tori in $S^3$---though this last assertion goes beyond the scope of this paper. An effort is made to intuitively motivate all necessary concepts including rotation, stereographic projection, and symmetry. | |
| dc.identifier | https://arxiv.org/abs/math/9810023 | |
| dc.identifier | http://arxiv.org/abs/math/9810023 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/77500 | |
| dc.subject | Metric Geometry | |
| dc.title | Rotations of the three-sphere and symmetry of the Clifford torus | |
| dc.type | text |