Hamiltonian vector fields on a space of curves on the 3-sphere
| dc.contributor.author | Ismail Hossain, Md | |
| dc.contributor.examiningcommittee | Clay, Adam (Mathematics) Muthukumarana, Saman (Statistics) | en_US |
| dc.contributor.supervisor | Krepski, Derek (Mathematics) | en_US |
| dc.date.accessioned | 2018-07-11T19:11:00Z | |
| dc.date.available | 2018-07-11T19:11:00Z | |
| dc.date.issued | 2018-07-11 | en_US |
| dc.date.submitted | 2018-07-11T18:11:11Z | en |
| dc.degree.discipline | Mathematics | en_US |
| dc.degree.level | Master of Science (M.Sc.) | en_US |
| dc.description.abstract | This thesis reviews aspects related to the integrability of a Hamiltonian system on a space of arc length parametrized curves on the unit sphere $S^3$ in $\mathbb{R}^4$ of a fixed length $L$. In particular, we find that the flow of the Hamiltonian vector field corresponding to the total torsion function $X(s) \mapsto \displaystyle\int_o^{L} \tau(s) ds$ generates the curve shortening equation. Additionally, we show that the total torsion function belongs to a hierarchy of Poisson commuting functions. | en_US |
| dc.description.note | October 2018 | en_US |
| dc.identifier.uri | http://hdl.handle.net/1993/33134 | |
| dc.language.iso | eng | en_US |
| dc.rights | open access | en_US |
| dc.subject | Mathematics | en_US |
| dc.title | Hamiltonian vector fields on a space of curves on the 3-sphere | en_US |
| dc.type | master thesis | en_US |